Independence Set Research Articles

Empowered through Labor and Buttressing Their Communities: Mayan Women and Coastal Migration, 1875-1965

Empowered through Labor and Buttressing Their Communities: Mayan Women and Coastal Migration, 1875-1965

Kekulé structures and the face independence number of a fullerene

We explore the relationship between Kekulé structures and maximum face independence sets in fullerenes: plane trivalent graphs with pentagonal and hexagonal faces. For the class of leap-frog fullerenes, we show that a maximum face independence set corresponds to a Kekulé structure with a maximum number of benzene rings and may be constructed by partitioning the pentagonal faces into pairs and 3-coloring the faces with the exception of a very few faces along paths joining paired pentagons. We also obtain some partial results for non-leap-frog fullerenes.

An Adjacency Criterion for the Prime Graph of a Finite Simple Group

In the paper we give an exhaustive arithmetic criterion of adjacency in prime graph $GK(G)$ for every finite nonabelian simple group $G$. By using this criterion for all finite simple groups an independence set with the maximal number of vertices, an independence set containing 2 with the maximal number of vertices, and the orders of these independence sets are given. We assemble this information in the tables at the end of the paper. Several applications of obtained results for various problems of finite group theory are considered.

The independence numbers of fullerenes and benzenoids

We explore the structure of the maximum vertex independence sets in fullerenes: plane trivalent graphs with pentagonal and hexagonal faces. At the same time, we will consider benzenoids: plane graphs with hexagonal faces and one large outer face. In the case of fullerenes, a maximum vertex independence set may constructed as follows: (i) Pair up the pentagonal faces. (ii) Delete the edges of a shortest path in the dual joining the paired faces to get a bipartite subgraph of the fullerene. (iii) Each of the deleted edges will join two vertices in the same cell of the bipartition; eliminating one endpoint of each of the deleted edges results in two independent subsets. The main part of this paper is devoted to showing that for a properly chosen pairing, the larger of these two independent subsets will be a maximum independent set. We also prove that the construction of a maximum vertex independence set in a benzenoid is similar with the dual paths between pentagonal faces replaced by dual circuits through the outside face. At the end of the paper, we illustrate this method by computing the independence number for each of the icosahedral fullerenes.

The Empowering Practice Programme at the University of the West of England

This article outlines the Empowering Practice programme at the University of the West of England ‐ its content and its educational approach. Students are staff working in local residential and day care services for people with learning difficulties. Many of them do not have the standard entry requirements for entry to higher education. An evaluation of the programme is described and its findings presented. Students' academic performance has been good. More important, students reported significant improvements in their self‐confidence and ability to implement the principles of rights, independence, choice and inclusion set out in Valuing People. This was confirmed both by immediate line managers and by senior managers in their employing agencies. Further, the higher education setting of the programme was seen by all stakeholder groups as contributing to stronger outcomes of this kind than NVQ programmes. The programme closely matches a range of LDAF units at Level 3.

Reclaiming history: women in the telegraph industry

In the mid-nineteenth century, women entered a challenging, competitive technological field: the telegraph industry. They competed directly with men, demanding, and occasionally getting, equal pay; they moved into both management and senior technical positions. Women telegraphers comprised a subculture of technically educated workers whose skills, mobility, and independence set them apart from their contemporaries. The story of women telegraph operators has remained untold, partly because the story of the telegraph itself has been forgotten, and partly because these women were so far ahead of their time. The paper provides an analysis of the role that women played in the telegraph industry, how they defined themselves as technical professionals, and how their work related to that of women in modern technical fields.

On fuzzy independence set systems

The concept of fuzzy pre-independence set system and that of fuzzy independence set system are introduced and investigated in this paper. The properties “to be closed”, “to be perfect” and “to be strongly regular” of a fuzzy independence set system are also considered. Several propositions concerning bases of closed perfect fuzzy independence set systems are presented. An important subclass of perfect fuzzy independence set systems, are fuzzy matroids, introduced by Goetschel and Voxman [Fuzzy Sets and Systems 27 (1988) 291; 31 (1989) 253].

An upper bound on the independence number of a graph computable in polynomial-time

An upper bound on the independence number of an undirected graph is presented. The bound is deduced by applying the theory of lagrangian duality to a quadratic formulation of the problem. A characterization of the graphs that attain the proposed bound and a heuristic for approaching the largest independence set of any graph are also given.

Superlinear bounds for matrix searching problems

Matrix searching in classes of totally monotone partial matrices has many applications in computer science, operations research, and other areas. This paper gives the first superlinear lower bound for matrix searching in classes of totally monotone partial matrices and also contains some new upper bounds for a class with applications in computational geometry and dynamic programming. The precise results of this paper are as follows. We show that any algorithm for finding row maxima or minima in totally monotone partial 2 n × n matrices with the property that the non-blank entries in each column form a contiguous segment, can be forced to evaluate Ω(nα(n)) entries of the matrix in order to find the row maxima or minima, where α( n) denotes the very slowly growing inverse of Ackermann's function. A similar result is obtained for n × 2 n matrices with contiguous non-blank segments in each row. The lower bounds are proved by introducing the concept of an independence set in a partial matrix and showing that any matrix searching algorithm for these types of partial matrices can be forced to evaluate every element in the independence set. A result involving lower bounds for Davenport-Schinzel sequences is then used to construct an independence set of size Ω(nα(n)) in the matrices of size 2 n × n and n × 2 n. We also give two algorithms to find row maxima and minima in totally monotone partial n × m matrices with the property that the non-blank entries in each column form a continuous segment ending at the bottom row. The first algorithm evaluates at most O( mα( n) + n) entries of the skyline matrix and performs at most that many comparisons, but may have O( mα( n)log log n + n) total running time. The second algorithm is simpler and has O( m log log n + n) total running time, but makes more comparisons, namely O( m log log n + n), than the first.