Color Classes Research Articles

COMPARATIVE ANTHROPOLOGICAL CHARACTERISTICS OF ATTIC WHITE-GROUND VASE PAINTING

Introduction. Of the numerous ceramic production centers of ancient Greece, the Attica region is notable for its continuous development of vase painting styles. Compared to the black-figure and red-figure painting techniques, the polychrome painting of Attic vases on a white-ground may indicate polymorphism in the pigmentation of the ancient Greeks. Materials and methods. The material was collected in digitized museum collections and thematic literature. The color and nature of the characters' hair were studied from vase painting and funerary painting. Anthroposcopic method and simple statistics were used. The significance of differences between groups was assessed using the chi-square test. Results and discussion. In all samples of Attic vase painting, the wavy nature of the hair is predominant, and this frequency does not change significantly over time. The highest frequency of straight nature of the hair (13.3%) is observed in white-ground vase painting. In comparison with the characters in vase paintings, modern Greeks have predominantly straight, lightly wavy hair, especially in women, and then wavy hair. For all style groups of Attic vase painting, no gender differences in nature of the hair were identified. The depiction of hair color on white-ground vase paintings of the early classical and classical times is significantly different: in the earlier vase painting, black and dark brown predominate, and in the later ones, brown/light brown and red-brown. The minimum frequency of dark shades of the hair is noted in Hellenistic funerary painting; it shows, like the white-ground vase painting of the classics, a lighter-pigmented population. The hair color of the modern Greek population is predominantly dark. Based on the hypothesis that the artist depicts familiar forms as traditional ones and reflects the anthropological characteristics of his group, the polymorphism of pigmentation and nature of the hair of the ancient and modern Greek populations is different. Conclusion. Groups of art sources that differ in chronology and style do not represent the hair pigmentation of the population of ancient Greece in the same way. To further study polymorphism of pigmentation of the ancient population, it is necessary to correct the methodology to correlate the actual colors used in vase/mural painting with the hair color classes of the traditional color scale, as well as the use of additional comparative materials.

Assessing Microplastics and Nanoparticles in the Surface Seawater of Venice Lagoon-Part I: Methodology of Research.

Microplastics (MPs) and nanoplastics (NPs) both represent significant concerns in environmental sciences. This paper aims to develop a convenient and efficient methodology for the detection and measurement of MPs and nanoparticles from surface seawater and to apply it to the water samples collected from the UNESCO site of Venice and its lagoon, more precisely in the Venice-Lido Port Inlet, Grand Canal under Rialto Bridge, and Saint Marc basin. In this study, MPs were analyzed through optical microscopy for their relative abundance and characterized based on their color, shape, and size classes, while the concentration and the mean of nanoparticles were estimated via the Nanoparticle Tracking Analysis technique. Bulk seawater sampling, combined with filtration through a cascade of stainless-steel sieves and subsequent digestion, facilitates the detection of MPs of relatively small sizes (size classes distribution: >1 mm, 1000-250 μm, 250-125 μm, 125-90 μm, and 90-32 μm), similar to the size of MPs ingested by marine invertebrates and fishes. A protocol for minimizing interference from non-plastic nanoparticles through evaporation, digestion, and filtration processes was proposed to enrich the sample for NPs. The findings contribute to the understanding of the extent and characteristics of MPs and nanoparticle pollution in the Venice Lagoon seawater, highlighting the potential environmental risks associated with these pollutants and the need for coordinated approaches to mitigate them. This article is based on scientific research carried out within the framework of the H2020 In-No-Plastic-Innovative approaches towards prevention, removal and reuse of marine plastic litter project (G.A. ID no. 101000612).

On Fall-Colorable Graphs

A fall k-coloring of a graph G is a proper k-coloring of G such that each vertex has at least one neighbor in each of the other color classes. A graph G which has a fall k-coloring is equivalent to having a partition of the vertex set V(G) in k independent dominating sets. In this paper, we first prove that for any fall k-colorable graph G with order n, the number of edges of G is at least (n(k−1)+r(k−r))/2, where r≡n(modk) and 0≤r≤k−1, and the bound is tight. Then, we obtain that if G is k-colorable (k≥2) and the minimum degree of G is at least k−2k−1n, then G is fall k-colorable and this condition of minimum degree is the best possible. Moreover, we give a simple proof for an NP-hard result of determining whether a graph is fall k-colorable, where k≥3. Finally, we show that there exist an infinite family of fall k-colorable planar graphs for k∈{5,6}.

The Ramsey Numbers of Squares of Paths and Cycles

The square $G^2$ of a graph $G$ is the graph on $V(G)$ with a pair of vertices $uv$ an edge whenever $u$ and $v$ have distance $1$ or $2$ in $G$. Given graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the minimum $N$ such that whenever the edges of the complete graph $K_N$ are coloured with red and blue, there exists either a red copy of $G$ or a blue copy of $H$.
 We prove that for all sufficiently large $n$ we have$$ R(P_{3n}^2,P_{3n}^2)=R(P_{3n+1}^2,P_{3n+1}^2)=R(C_{3n}^2,C_{3n}^2)=9n-3\mbox{ and } R(P_{3n+2}^2,P_{3n+2}^2)=9n+1.$$
 We also show that for any $\gamma>0$ and $\Delta$ there exists $\beta>0$ such that the following holds: If $G$ can be coloured with three colours such that all colour classes have size at most $n$, the maximum degree $\Delta(G)$ of $G$ is at most $\Delta$, and $G$ has bandwidth at most $\beta n$, then $R(G,G)\le (3+\gamma)n$.

Locating Chromatic Number of Middle Graph of Path, Cycle, Star, Wheel, Gear and Helm Graphs

Let \(c\) be a proper \(k\)-coloring of a connected graph \(G\) and \(\pi=\{S_{1},S_{2},\ldots,S_{k}\}\) be an ordered partition of the vertex set \(V(G)\) into the resulting color classes, where \(S_{i}\) is the set of all vertices that receive the color \(i\). For a vertex \(v\) of \(G\), the color code \(c_{\pi}(v)\) of \(v\) with respect to \(\pi\) is the ordered \(k\)-tuple \(c_{\pi}(v)=(d(v,S_{1}),d(v,S_{2}),\ldots,d(v,S_{k}))\), where \(d(v,S_{i})=min\{d(v,u):\textit{ } u\in S_{i}\}\) for \(1\leqslant i \leqslant k\). If all distinct vertices of \(G\) have different color codes, then \(c\) is called a locating coloring of \(G\). The locating chromatic number is the minimum number of colors needed in a locating coloring. In this paper, we determine the locating-chromatic number for the middle graphs of Path, Cycle, Wheel, Star, Gear and Helm graphs.

On uniquely packable trees

An i-packing in a graph G is a set of vertices that are pairwise at distance more than i. A packing colouring of G is a partition X = {X 1, X 2, . , X k } of V(G) such that each colour class Xi is an i-packing. The minimum order k of a packing colouring is called the packing chromatic number of G, denoted by χρ (G). In this paper we investigate the existence of trees T for which there is only one packing colouring using χρ (T) colours. For the case χρ (T) = 3, we completely characterise all such trees. As a by-product we obtain sets of uniquely 3-χρ -packable trees with monotone χρ -colouring and non-monotone χρ -colouring respectively.

Ramsey numbers upon vertex deletion

AbstractGiven a graph , its Ramsey number is the minimum so that every two‐coloring of contains a monochromatic copy of . It was conjectured by Conlon, Fox, and Sudakov that if one deletes a single vertex from , the Ramsey number can change by at most a constant factor. We disprove this conjecture, exhibiting an infinite family of graphs such that deleting a single vertex from each decreases the Ramsey number by a super‐constant factor. One consequence of this result is the following. There exists a family of graphs so that in any Ramsey coloring for (i.e., a coloring of a clique on vertices with no monochromatic copy of ), one of the color classes has density .

First Fit Algorithm: A Graph Coloring Approach to Conflict-Free University Course Timetabling

Aims: Tackling scheduling issues with the most optimal graph coloring algorithm has consistently posed significant difficulties. The university scheduling problem can be expressed as a graph coloring problem, where courses are depicted as vertices and the connections between courses that have common students or teachers are represented as edges. Subsequently, the task at hand is to assign the vertices with the minimum number of colors. In order to accomplish this task, this paper present a graph coloring technique to conflict free university course timetabling using first fit algorithms.
 Methodology: The conflict graph is partitioned into a set of independent color classes to be assigned time slots and transformed into a conflict-free timetable. The Ladoke Akintola University of Technology (LAUTECH) University Course Timetabling Data was adopted. The allocation of venue based on the allotted time slots is done using first fit packing algorithm. The proposed model is implemented using Python programming language. The developed model had courses being represented as vertices and edges. The course conflict graph was created based on the acquired dataset using vertices-edges relationship diagram. The implemented model is evaluated in terms of Halstead complexity metrics: Program Volume (PV), Program Length (PL), Program Effort (PE), Program Difficulty (PD) and Execution Time (ET). The PV, PL, PE, PD and ET values obtained for the implemented model are 18.45kbits, 0.51, 1037684, 1.97 and 20.45 secs, respectively.
 Conclusion: The proposed model shows a significant improvement over the existing models by producing conflict-free course timetabling problem with better evaluation results. This work will be highly useful in solving various scheduling, optimization and NP-hard related computational problems.

On the total chromatic number of the direct product of cycles and complete graphs

A k-total coloring of a graph G is an assignment of k colors to the elements (vertices and edges) of G so that adjacent or incident elements have different colors. The total chromatic number is the smallest integer k for which G has a k-total coloring. The well known Total Coloring Conjecture states that the total chromatic number of a graph is either Δ(G) + 1 (called Type 1) or Δ(G) + 2 (called Type 2), where Δ(G) is the maximum degree of G. We consider the direct product of complete graphs Km × Kn. It is known that if at least one of the numbers m or n is even, then Km × Kn is Type 1, except for K2 × K2. We prove that the graph Km × Kn is Type 1 when both m and n are odd numbers, by using that the conformable condition is sufficient for the graph Km × Kn to be Type 1 when both m and n are large enough, and by constructing the target total colorings by using Hamiltonian decompositions and a specific color class, called guiding color. We additionally apply our technique to the direct product Cm × Kn of a cycle with a complete graph. Interestingly, we are able to find a Type 2 infinite family Cm × Kn, when m is not a multiple of 3 and n = 2. We provide evidence to conjecture that all other Cm × Kn are Type 1.

Microplastics in rocky shore mollusks of different feeding habits: An assessment of sentinel performance

Microplastics (MPs) accumulation in rocky shore organisms has limited knowledge. This study investigated MPs accumulation in filter-feeding oysters, herbivorous limpets and carnivorous snails to assess their performance as sentinel species in the MPs trophic transfer. The samples were obtained along a contamination gradient in the Santos Estuarine System, Brazil. All three studied species showed MPs concentrations related to the contamination gradient, being the oysters the species that showed the highest levels, followed by limpets and snails (average of less and most contaminated sites of 1.06–8.90, 2.28–5.69 and 0.44–2.10 MP g−1, respectively), suggesting that MPs ingestion rates are linked to feeding habits. MPs were mainly polystyrene and polyacetal. The polymer types did not vary among sites nor species. Despite minor differences in percentages and diversity of size, shape, and color classes, the analyzed species were equally able to demonstrate dominance of small, fiber, transparent, black and blue MPs. Thus, oysters, limpets, and snails are proposed as sentinels of MPs in monitoring assessments.

Computer Vision-Aided Intelligent Monitoring of Coffee: Towards Sustainable Coffee Production

Earlier, researchers have employed computer vision-based automatic fruit detection to estimate coffee yield at the time of harvest, however, studies on the on-plant quantification of the coffee fruit are scarce. In this study, the latest version of the state-of-the-art algorithm YOLOv7 (You Only Look Once) was used for the first time. YOLOv7 was trained with 324 annotated images of fruit bearing coffee branches followed by its evaluation with 82 annotated images as validation data (supervised method) and then tested through raw images (unannotated) as test data. Meanwhile, the K-means models were trained which led to machine-generated color classes of coffee fruit for semi-supervised image annotation. Consequently, the developed model efficiently analyzed the test data with an mAP@.5 (mean average precision) of 0.89. Strikingly, our innovative semi-supervised method with an mAP@.5 of 0.77 for multi-class mode surpassed the supervised method which had mAP@.5 of only 0.60, leading to faster and more accurate annotation. While testing the yield estimation of the model in two plots, an average error of 3.78% was recorded between the predicted (pre-harvest) and ground truth (harvest) data for binary class mode. The average error for multi-class data was recorded as 3.87% for green, 3.445% for green-yellow, 5.09% for cherry-raisin, and 2.51% for dry fruits. This AI-based technology when integrated with other tools such as UAV would efficiently remotely monitor coffee field for informed decision about irrigation, fertilizer application and other measures of timely field management, hence advancing precision agriculture. Moreover, this machine learning intelligent model can be tailored for various other fruit farming.

A Note on Ramsey Numbers Involving Large Books

For graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the minimum integer $N$ such that any red/blue edge coloring of $K_N$ contains either a red $G$ or a blue $H$. Let $\chi(G)$ be the chromatic number of $G$, and $s(G)$ the minimum size of a color class over all proper vertex colorings of $G$ with $\chi(G)$ colors. A connected graph $H$ is called $G$-{\em good} if $R(G,H)= (\chi(G)-1)(|H|-1)+s(G)$. For graphs $G$ and $H$, it is shown $K_p+nH$ is $(K_2+G)$-{\em good}, where $n$ is double-exponential in terms of $p,|G|,|H|$, and $K_p+nH$ is $C_{2m+1}$-{\em good} for $n\ge (100q)^{8q^3}$, where $q=\max\{m,p,|H|\}$. Both proofs are short that avoids using the regularity method.

Microplastics in Qinghai-Tibet Plateau and Yunnan-Guizhou Plateau lakes, China

As an emerging environmental pollutant, microplastics (MPs) have received widespread attention. Recently, studies examining microplastic pollution in plateau lakes have been increasing, but few have examined the distributions, sources, and fates of MPs in different plateau areas. In this work, the abundances and characteristics of MPs in surface waters and sediments in lakes of the Qinghai-Tibet Plateau (QTP) and Yunnan-Guizhou Plateau (YGP) were systematically investigated. The abundances of MPs in the lakes of the QTP ranges within 0.05–1.8 n/L in surface waters and 10–2643.7 n/kg in sediments. In the lakes of the YGP, the abundances of MPs ranged within 1.3–10.1 n/L in surface waters and 171.7–4260 n/kg in sediments. The dominant shape, color, and size class of MPs were fiber, transparent, and 0–0.5 mm in plateau lakes, respectively. MPs were mainly composed of polypropylene, polyethylene, and polyethylene terephthalate polymers. The different sources of MPs in the QTP and YGP lakes were mainly due to differences in human activities. The primary sources of microplastic pollution in the lakes of the QTP were tourism and atmospheric transport, while sewage discharge, agriculture, and fishing activities were the main sources of MPs in urban lakes of the YGP. Although the level of microplastic pollution in plateau lakes was relatively low, the sources should be identified and monitored so that the effects and extent of microplastic pollution in these fragile environments can be fully understood. This study provides a valuable dataset and theoretical basis for subsequent research on microplastic pollution in plateau lakes.

On the oriented coloring of the disjoint union of graphs

Let G⃗ = (V, A) be an oriented graph and G the underlying graph of G⃗. An oriented k-coloring of G⃗ is a partition of V into k color classes, such that there is no pair of adjacent vertices belonging to the same class and all the arcs between a pair of color classes have the same orientation. The smallest k such that G⃗ admits an oriented k-coloring is the oriented chromatic number χo(G⃗) = k of G⃗. The oriented chromatic number χo(G) of the undirected graph G is the maximum of χo(G⃗) for all orientations G⃗ of G. Oriented chromatic number of the product of two graphs G1, G2 was widely studied, but the disjoint union G1 ∪ G2 has not yet been considered. In this article we proved bounds for the oriented chromatic number of any two oriented graphs and we also proved that given two complete graphs Kn and Km with n ≥ m, there is a real number α ∈ (1, 3) such that χo(Kn ∪ Km) = n + m − α log2(m). Additionally, we established exact values of the union of one complete graph with one cycle and of one complete graph with a forest.

Dominator coloring of Kneser graph

A dominator coloring (briefly DC) of a graph G is a proper coloring such that each vertex dominates every vertex of at least one color class (possibly its own class). The dominator chromatic number χd(G) of G is the smallest cardinality of color classes in a DC of G. By using Steiner triple systems, in this paper, we establish that the dominator coloring of the Kneser graph KG(n, 2) is n for n ≥ 5.

A Study on Variants of Status Unequal Coloring in Graphs and Its Properties

Let be a simple connected graph with vertex set and edge set . The status of a vertex is defined as ∑q≠pd(p, q). A subset of is called a status unequal dominating set (stu‐dominating set) of ; for every , there exists p in such that p and q are adjacent and st(p) ≠ st(q). Among the most admired, extensively explored, and extensively discussed topics in the field of graph theory is graph coloring. This article recommends a new research study on the topic of incorporating stu‐dominating set with coloring. Diverse coloring variants can be found in literature, some of which serve as inspiration is chromatic number, dominator coloring, color class domination, and colorful dominating sets. A novel study on the topic of incorporating stu‐dominating set with coloring is suggested in this article. The stu‐chromatic number, stu‐dominator coloring, stu‐color class domination, and colorful stu‐domination have thus been explored and investigated. For each parameter introduced, the minimum cardinality of certain standard classes of graphs, bounds, and characterization results was explored.

Total dominator total coloring of a graph

Here, we initiate to study the total dominator total coloring of a graph which is a total coloring of the graph such that each object of the graph is adjacent or incident to every object of some color class. In more details, while in section 2 we present some tight lower and upper bounds for the total dominator total chromatic number of a graphs in terms of some parameters such as order, size, the total dominator chromatic and total domination numbers of the graph and its line graph, in section 3 we restrict our to trees and present a Nordhaus-Gaddum-like relation for trees. Finally in last section we show that there exist graphs that their total dominator total chromatic numbers are equal to their orders.

Effect of caramel colors addition on the color, physicochemical properties, and flavor of Huangjiu

Caramel color is a food colorant widely used in the fermented beverage industries. In this context, this study investigated the effects of caramel color on the quality of Huangjiu in terms of color, physicochemical properties, sensory characteristics, and the release of volatile organic compounds (VOCs). The results showed that Class IV caramel colors with the highest color intensity had the lowest coloring ability in Huangjiu due to precipitation. Caramel colors significantly affected the total sugar, titratable acidity, and amino nitrogen of Huangjiu. Sensory analyses indicated that the three classes of caramel colors significantly affected 10 sensory attributes and the aroma release of Huangjiu. The headspace concentrations of the 40 VOCs in Huangjiu changed significantly. Principal component analysis (PCA) and cluster analysis showed that Classes I and III caramel colors had similar effects on the VOCs in Huangjiu. Partial least-squares discriminant analysis (PLS-DA) showed that 9 compounds made important contributions to distinguishing different classes of caramel-colored Huangjiu samples. This study provides a theoretical foundation for the scientific application of caramel color in Huangjiu and other fermented food industries.

Strongly Proper Connected Coloring of Graphs

We study a new variant of connected coloring of graphs based on the concept of strong edge coloring (every color class forms an induced matching). In particular, an edge-colored path is strongly proper if its color sequence does not contain identical terms within a distance of at most two. A strong proper connected coloring of G is the one in which every pair of vertices is joined by at least one strongly proper path. Let spc(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\,\ extrm{spc}\\,}}(G)$$\\end{document} denote the least number of colors needed for such coloring of a graph G. We prove that the upper bound spc(G)≤5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\,\ extrm{spc}\\,}}(G)\\le 5$$\\end{document} holds for any 2-connected graph G. On the other hand, we demonstrate that there are 2-connected graphs with arbitrarily large girth satisfying spc(G)≥4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\,\ extrm{spc}\\,}}(G)\\ge 4$$\\end{document}. Additionally, we prove that graphs whose cycle lengths are divisible by 3 satisfy spc(G)≤3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\,\ extrm{spc}\\,}}(G)\\le 3$$\\end{document}. We also consider briefly other connected colorings defined by various restrictions on color sequences of connecting paths. For instance, in a nonrepetitive connected coloring of G, every pair of vertices should be joined by a path whose color sequence is nonrepetitive, that is, it does not contain two adjacent identical blocks. We demonstrate that 2-connected graphs are 15-colorable, while 4-connected graphs are 6-colorable, in the connected nonrepetitive sense. A similar conclusion with a finite upper bound on the number of colors holds for a much wider variety of connected colorings corresponding to fairly general properties of sequences. We end the paper with some open problems of concrete and general nature.

Revisiting semistrong edge‐coloring of graphs

AbstractA matching in a graph is semistrong if every edge of has an endvertex of degree one in the subgraph induced by the vertices of . A semistrong edge‐coloring of a graph is a proper edge‐coloring in which every color class induces a semistrong matching. In this paper, we continue investigation of properties of semistrong edge‐colorings initiated by Gyárfás and Hubenko. We establish tight upper bounds for general graphs and for graphs with maximum degree 3. We also present bounds about semistrong edge‐coloring which follow from results regarding other, at first sight nonrelated, problems. We conclude the paper with several open problems.