Bipartite Graph Research Articles

On Hamilton Laceability and Random Hamiltonian-t*– Laceablity of Total Transformation Graph G-++

A connected graph is called Hamiltonian if contains a spanning cycle and if a graph contains a spanning path between arbitrary pair of its vertices is called Hamilton-connected. A bipartite graph is called Hamilton-laceable if there exist Hamiltonian path between vertices of different partite sets and a graph is random Hamiltonian-– laceable if there exists a Hamiltonian path for at least one pair for distance. In this paper, we have studied the Hamiltonian laceble and random Hamiltonian-– laceable graphs of total transformation graph of graphs viz. path , cycle , complete bipartite graph , n-dimensional convex polytopes , and gn .

Matching Cuts in Graphs of High Girth and H-Free Graphs

Abstract The (Perfect) Matching Cut problem is to decide if a connected graph has a (perfect) matching that is also an edge cut. The Disconnected Perfect Matching problem is to decide if a connected graph has a perfect matching that contains a matching cut. Both Matching Cut and Disconnected Perfect Matching are -complete for planar graphs of girth 5, whereas Perfect Matching Cut is known to be -complete even for subcubic bipartite graphs of arbitrarily large fixed girth. We prove that Matching Cut and Disconnected Perfect Matching are also -complete for bipartite graphs of arbitrarily large fixed girth and bounded maximum degree. Our result for Matching Cut resolves a 20-year old open problem. We also show that the more general problem d -Cut, for every fixed $$d\ge 1$$ d ≥ 1 , is -complete for bipartite graphs of arbitrarily large fixed girth and bounded maximum degree. Furthermore, we show that Matching Cut, Perfect Matching Cut and Disconnected Perfect Matching are -complete for H-free graphs whenever H contains a connected component with two vertices of degree at least 3. Afterwards, we update the state-of-the-art summaries for H-free graphs and compare them with each other, and with a known and full classification of the Maximum Matching Cut problem, which is to determine a largest matching cut of a graph G. Finally, by combining existing results, we obtain a complete complexity classification of Perfect Matching Cut for $$\mathcal{H}$$ H -subgraph-free graphs where $$\mathcal{H}$$ H is any finite set of graphs.

Convex Nonnegative Matrix Factorization on Bipartite Graph

In this paper, we propose a novel convex nonnegative matrix factorization (CNMF) method to learn a bipartite graph with exactly k connected compo-nents, where k is the number of clusters. The new bipartite graph learned in our model approximates the original graph but maintains an explicit cluster struc-ture, from which we can immediately get the clustering results. Besides, inspired by self-expressive assumption of the data and subspace clustering, we added ad-ditional constraints to further recover global structural information of the data. Multiplicative updating rules are developed. The superiority of our method over the effectiveness and efficiency is demonstrated by extensive experiments.

On the complexity of perfect Roman domination and perfect double Roman domination

For a graph [Formula: see text] and a function [Formula: see text], let [Formula: see text] ([Formula: see text]) be the set of vertices assigned the value [Formula: see text] by [Formula: see text]. A perfect Roman dominating function on a graph [Formula: see text] is a function [Formula: see text] satisfying the condition that every vertex [Formula: see text] is adjacent to exactly one vertex [Formula: see text]. A perfect double Roman dominating function of a graph [Formula: see text] is a function [Formula: see text] satisfying the condition that (1) every vertex [Formula: see text] is adjacent to exactly two vertices in [Formula: see text] and no vertex in [Formula: see text], or exactly one vertex in [Formula: see text] and no vertex in [Formula: see text]; (2) If [Formula: see text], then [Formula: see text] is adjacent to exactly one vertex in [Formula: see text] and no vertex in [Formula: see text]. In this paper, we prove that the decision problem associated to perfect Roman domination problem is NP-complete even when restricted to double star convex bipartite graphs, and the decision problem associated to perfect double Roman domination problem is NP-complete for comb convex bipartite graphs. We also prove that the decision problem associated to a similar Roman domination variant, namely minimum independent Roman domination problem is NP-complete even when restricted to double star convex bipartite graphs.

Computational analysis of learning in young and ageing brains

Learning and memory are fundamental processes of the brain which are essential for acquiring and storing information. However, with ageing the brain undergoes significant changes leading to age-related cognitive decline. Although there are numerous studies on computational models and approaches which aim to mimic the learning process of the brain, they often concentrate on generic neural function exhibiting the potential need for models that address age-related changes in learning. In this paper, we present a computational analysis focusing on the differences in learning between young and old brains. Using a bipartite graph as an artificial neural network to model the synaptic connections, we simulate the learning processes of young and older brains by applying distinct biologically inspired synaptic weight update rules. Our results demonstrate the quicker learning ability of young brains compared to older ones, consistent with biological observations. Our model effectively mimics the fundamental mechanisms of the brain related to the speed of learning and reveals key insights on memory consolidation.

The modular chromatic number of Cartesian product and join of graphs

A vertex coloring [Formula: see text] is defined as, for every [Formula: see text] and [Formula: see text] the sum of the colors of the neighbors of [Formula: see text] and [Formula: see text] that are different in [Formula: see text] The smallest [Formula: see text] for which [Formula: see text] has a modular [Formula: see text]-coloring is the modular chromatic number of [Formula: see text]. In this paper, we calculate the modular chromatic number of [Formula: see text]-regular circulant graphs and [Formula: see text] where [Formula: see text] is a bipartite graph and [Formula: see text] and we give the partial solution to the Problem 1 and it was posed in [R. Rajarajachozhan and R. Sampathkumar, Modular coloring of the Cartesian products [Formula: see text] and [Formula: see text] Discr. Math. Algor. Appl. 9(6) (2017) 1750075]. Also, we prove the Problem 2 partially and it posed in [N. Paramaguru and R. Sampathkumar, Modular colorings of join of two special graphs, Electron. J. Graph Theory Appl. 2(2) (2014) 139–149]. Furthermore, we find [Formula: see text] where [Formula: see text] is either bipartite graph or [Formula: see text]

Some new results on anti-adjacency spectra of regular graphs

The anti-adjacency matrix [Formula: see text] of a simple graph [Formula: see text] with [Formula: see text], is a square matrix of order [Formula: see text] with rows and columns indexed by [Formula: see text], where the [Formula: see text]-entry [Formula: see text] is [Formula: see text], if the vertices [Formula: see text] and [Formula: see text] are not adjacent to each other and [Formula: see text], otherwise. The [Formula: see text]- entry of [Formula: see text] is [Formula: see text]. The anti-adjacency eigenvalues of [Formula: see text] are the eigenvalues obtained from the matrix [Formula: see text] and the corresponding spectra is called the anti-adjacency spectra of [Formula: see text], denoted by [Formula: see text]-spec([Formula: see text]). In this paper, we discuss the anti-adjacency spectra of join and disjoint union of regular graphs. The anti-adjacency spectra of bipartite regular graphs, line graphs of regular graphs and strongly regular graphs are also discussed.

Packing two copies of a tree into a bipartite graph with restrained maximum degree

Packing two copies of a tree into a bipartite graph with restrained maximum degree

Extremal function of two independent chorded cycles in a bipartite graph

Extremal function of two independent chorded cycles in a bipartite graph

When bipartite graph learning meets anomaly detection in attributed networks: Understand abnormalities from each attribute.

When bipartite graph learning meets anomaly detection in attributed networks: Understand abnormalities from each attribute.

Resonance graphs of plane bipartite graphs as daisy cubes

Resonance graphs of plane bipartite graphs as daisy cubes

Hop $k$-Rainbow Domination in Graphs

Let \( G = (V(G), E(G)) \) be a graph. A function \( f \) that assigns to each vertex \linebreak of $G$ a subset of colors from the set \( \{1, 2, \dots, k\} \), i.e., \( f : V(G) \rightarrow P(\{1, 2, 3, \dots, k\}) \), is called a \textit{hop \( k \)-rainbow dominating function} (H$k$RDF) of \( G \) if for every vertex \( v \in V(G)\) with $f(v)= \varnothing$, we have \( \bigcup_{u \in N^{2}_{G}(v)} f(u) = \{1, 2, \dots, k\} \) where $N^{2}_{G}(v)$ is the set of vertices of $G$ at distance two from $v$. The \textit{weight} of \( f \), denoted \( w(f) \), is defined as \( w(f) = \sum_{x \in V(G)} |f(x)| \). The \textit{hop \( k \)-rainbow domination number} of \( G \), denoted \( \gamma_{hrk}(G) \), is the minimum weight of a hop \( k \)-rainbow dominating function of \( G \). A hop $k$-rainbow dominating function of $G$ with weight $\gamma_{hrk}(G)$ is a $\gamma_{hrk}$-function of $G$. In this paper, we initiate the study of hop \( k \)-rainbow domination in graphs. We begin by exploring fundamental properties of this parameter and then establish various bounds on \( \gamma_{hrk}(G) \). Furthermore, we identify the graphs for which \( \gamma_{hrk}(G) = n \) and determine exact values for certain graph classes, including complete graphs, complete bipartite graphs, paths, and cycles. Additionally, for any positive integer \( a \), we construct connected graphs satisfying \(\gamma_{hr2}(G) = \gamma_{r2}(G) = a.\) Finally, we provide a characterization of all graphs where \( \gamma_{hr2}(G) = n \).

Forcing Clique Domination in Graphs

The clique domination number of some special graphs such as paths, cycles, complete graphs, generalized wheels, generalized fans, and complete bipartite graphs is presented. The forcing clique domination number of these graphs, along with binary operations such as join, corona, and lexicographic product of two graphs, is also determined. Connected graphs with forcing clique domination number equal to $0$, $1$, or $a$, where $a$ is greater than $1$ but less than the clique domination number, are characterized. Necessary and sufficient conditions for the forcing clique domination number to be equal to the clique domination number are given. Since some of the graphs in this study do not have a clique dominating set, the forcing clique domination number is undefined in those cases.

A location semantic privacy protection model based on spatial influence

The utilization of numerous location-based intelligent services yields massive traffic trajectory data. Mining such data unveils internal and external user features, offering significant application value across various domains. Nonetheless, while trajectory data mining enhances user convenience, it also exposes their privacy to potential breaches. To address the problem that existing traffic trajectory privacy protection methods rarely consider the location semantics and the spatial influence of interest points when constructing k-anonymity sets, which makes user trajectories vulnerable to attacks, a Location Semantic Privacy Protection Model based on Spatial Influence (LSPPM-SI) is proposed to resist semantic attacks. Firstly, a location semantic mining algorithm is proposed to classify the stopovers based on positional semantics, thereby simplifying the semantic information contained in user trajectories. Secondly, a diversified semantic dummy location selecting algorithm is proposed to resist semantic attacks. To enhance the availability of traffic trajectory data while safeguarding location semantics, a Hilbert curves is used to reduce the area of anonymous regions, and a diversified semantic anonymous set is constructed. Thirdly, the spatial influence of interest points is defined and used to verify the rationality of dummy trajectories within the anonymous trajectory set, thereby preventing attackers from identifying dummy trajectories. Finally, the problem of synthesizing dummy trajectories is transformed into a matching problem for directed bipartite graphs and the optimal k-anonymity set is obtained using the Kuhn Munkres algorithm. Experimental results demonstrate that the proposed model improves traffic trajectory data availability and semantic protection performance by 14% and 46.5%, respectively, compared to traditional models.

Hypergraph removal with polynomial bounds

Abstract Given a fixed k-uniform hypergraph F, the F-removal lemma states that every hypergraph with few copies of F can be made F-free by the removal of few edges. Unfortunately, for general F, the constants involved are given by incredibly fast-growing Ackermann-type functions. It is thus natural to ask for which F one can prove removal lemmas with polynomial bounds. One trivial case where such bounds can be obtained is when F is k-partite. Alon proved that when $k=2$ (i.e. when dealing with graphs), only bipartite graphs have a polynomial removal lemma. Kohayakawa, Nagle and Rödl conjectured in 2002 that Alon’s result can be extended to all $k\gt2$ , namely, that the only $k$ -graphs $F$ for which the hypergraph removal lemma has polynomial bounds are the trivial cases when F is k-partite. In this paper we prove this conjecture.

Reduce-then-Optimize for the Fixed-Charge Transportation Problem

Research on addressing combinatorial optimization (CO) problems with machine learning (ML) is thriving with a strong focus on replacing exact but slow solvers with faster ML oracles. However, developing accurate and generalizable predictors remains challenging. We investigate a different paradigm, called reduce-then-optimize, that uses ML to reduce the problem complexity for a subsequent CO solver by predicting a relevant subset of variables. We apply this paradigm to the fixed-charge transportation problem (FCTP), an important problem class in logistics and transportation. To obtain a high-quality and problem size-agnostic predictor, we employ a tailored bipartite graph neural network (GNN). We evaluate the performance of our reduce-then-optimize pipeline on various FCTP benchmark data sets to analyze the impact of different instance characteristics, such as the supply-demand ratio or the predominance of the fixed costs, on the problem difficulty and predictability. This includes FCTP variants with edge capacities, fixed-step costs, and blending constraints. The GNN shows good prediction and generalization capabilities that translate into high-quality solutions across all data sets with optimality gaps below 1%, decreasing runtimes of a state-of-the-art mixed-integer linear programming by 80%–95%. When runtimes are limited, the problem reduction provides an effective reduction of the search space, which leads to better solutions in comparison with solving the full problem. Similarly, we systematically improve the solution quality and convergence of two established meta-heuristics by applying our reduce-then-optimize pipeline. As the GNN-based reduce-then-optimize pipeline can be easily adapted to support additional constraints and objectives, it constitutes a flexible and robust solution approach for FCTP solving in practice. Funding: This research was supported by the Deutsche Forschungsgemeinschaft (German Research Foundation) as part of the research group Advanced Optimization in a Networked Economy [Grant GRK2201/277991500]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0407 .

Assigning Candidate Tutors to Modules: A Preference Adjustment Matching Algorithm (PAMA)

Matching problems arise in various settings where two or more entities need to be matched—such as job applicants to positions, students to colleges, organ donors to recipients, and advertisers to ads slots in web advertising platforms. This study introduces the preference adjustment matching algorithm (PAMA), a novel matching framework that pairs elements, which conceptually represent a bipartite graph structure, based on rankings and preferences. In particular, this algorithm is applied to tutor–module assignment in academic settings, and the methodology is built on four key assumptions where each module must receive its required number of candidates, candidates can only be assigned to a module once, eligible candidates based on ranking and module capacity must be assigned, and priority is given to mutual first-preference matches with institutional policies guiding alternative strategies when needed. PAMA operates in iterative rounds, dynamically adjusting modules and tutors’ preferences while addressing capacity and eligibility constraints. The distinctive innovative element of PAMA is that it combines concepts of maximal and stable matching, pending status and deadlock resolution into a single process for matching tutors to modules to meet the specific requirements of academic institutions and their constraints. This approach achieves balanced assignments by adhering to ranking order and considering preferences on both sides (tutors and institution). PAMA was applied to a real dataset provided by the Hellenic Open University (HOU), in which 3982 tutors competed for 1906 positions within 620 modules. Its performance was tested through various scenarios and proved capable of effectively handling both single-round and multi-round assignments. PAMA effectively handles complex cases, allowing policy-based resolution of deadlocks. While it may lose maximality in such instances, it converges to stability, offering a flexible solution for matching-related problems.

Unraveling Disease-Associated PIWI-Interacting RNAs with a Contrastive Learning Methods.

PIWI-interacting RNAs (piRNAs) are a class of small, non-coding RNAs predominantly expressed in the germ cells of animals and play a crucial role in maintaining genomic integrity, mediating transposon suppression, and ensuring gene stability. Beyond their functions in reproductive cells, piRNAs also play roles in various human diseases, including cancer, suggesting their potential as significant biomarkers critical for disease diagnosis and treatment. Wet-lab methods to identify piRNA-disease associations require substantial resources and are often hit-or-miss. With advancements in computational technologies, an increasing number of researchers are employing computational methods to efficiently predict potential piRNA-disease associations. The sparsity of data in piRNA-disease association studies significantly limits model performance improvement. In this study, we propose a novel computational model, iPiDA_CL, to predict potential piRNA-disease associations through contrastive learning methods, which do not require negative samples. The model represents piRNA-disease association pairs as a bipartite graph and computes the initial embeddings of piRNAs and diseases using Gaussian kernel similarity, with features updated via LightGCN. Based on the siamese network framework, iPiDA_CL constructs online and target networks and employs data augmentation in the target network to build a contrastive learning objective that optimizes model parameters without introducing negative samples. Finally, cross-prediction methods are used to calculate specific piRNA-disease association scores. A series of experimental results demonstrate that iPiDA_CL surpasses state-of-the-art methods in both performance and computational efficiency. The application of iPiDA_CL to the miRNA-disease association dataset underscores its versatility across various ncRNA-disease association task. Furthermore, a case study highlights iPiDA_CL as an efficient and promising tool for predicting piRNA-disease associations.

Application and Research of Intelligent Algorithms in Scheduling Optimization of Civil Engineering Projects

Efficient scheduling optimization is a critical component of resource management in civil engineering projects, which often involve dynamic and complex environments. Traditional scheduling approaches face challenges in addressing large-scale constraints, real-time adaptability, and the combinatorial nature of tasks, leading to resource underutilization and delays. To address these issues, this study proposes a novel Adaptive Scheduling Framework (ASF) integrated with a Dynamic Task Allocation Strategy (DTAS) tailored specifically for civil engineering applications. The ASF employs graph-based task-resource modeling and multi-objective optimization to manage the scalability and flexibility required in construction projects. By representing scheduling problems as bipartite graphs, the framework captures temporal dynamics, task dependencies, and resource constraints to achieve a balance between priority and feasibility. The DTAS enhances scheduling efficiency by introducing dynamic task prioritization, iterative conflict resolution, and real-time feedback-driven refinement. Experimental results, focused on civil engineering scenarios, demonstrate that the proposed methods significantly reduce project completion time, improve resource utilization, and adapt effectively to changes in construction requirements and resource availability. This study underscores the transformative potential of intelligent algorithms in optimizing scheduling for civil engineering project management and other resource-intensive domains.

The distance Seidel matrix of connected graphs

For a connected graph G, we present the concept of a new graph matrix related to its distance and Seidel matrix, called distance Seidel matrix D S ( G ) . Suppose that the eigenvalues of D S ( G ) be ∂ 1 S ( G ) ≥ ⋯ ≥ ∂ n S ( G ) . In this article, we establish a relationship between the distance Seidel eigenvalues of a graph with its distance and adjacency eigenvalues. We characterize all the connected graphs with ∂ 1 S ( G ) = 3. Also, we determine different bounds for the distance Seidel spectral radius and distance Seidel energy. We analyze the effect of edge deletion on the distance Seidel energy of the complete bipartite graph. Moreover, we obtain the distance Seidel spectra of different graph operations such as join, cartesian product, lexicographic product, and unary operations like the double graph and extended double cover graph. We give various families of distance Seidel cospectral and distance Seidel integral graphs as an application.