Results 1 to 10 of about 983,866 (300)
The expected values of the total numbers of independent edge sets and independent sets in random alpha-type pentagonal chains [PDF]
Heliyon, 2023 A independent edge set of G containing mutually independent edges is also called a matching of G. The total numbers of matchings and independent sets of a graph G, namely, the Hosoya index and the Merrifield-Simmons index, respectively, are two important
Lina Wei, Hong Bian, Haizheng Yu
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A Generalized Information-Theoretic Approach for Bounding the Number of Independent Sets in Bipartite Graphs [PDF]
Entropy, 2021 This paper studies the problem of upper bounding the number of independent sets in a graph, expressed in terms of its degree distribution. For bipartite regular graphs, Kahn (2001) established a tight upper bound using an information-theoretic approach ...
Igal Sason
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On Independent [1, 2]-Sets in Trees [PDF]
Discussiones Mathematicae Graph Theory, 2018 An [1, k]-set S in a graph G is a dominating set such that every vertex not in S has at most k neighbors in it. If the additional requirement that the set must be independent is added, the existence of such sets is not guaranteed in every graph.
Aleid Sahar A. +2 more
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Fair Packing of Independent Sets [PDF]
Combinatorial Algorithms, 2020 In this work we add a graph theoretical perspective to a classical problem of fairly allocating indivisible items to several agents. Agents have different profit valuations of items and we allow an incompatibility relation between pairs of items described in terms of a conflict graph.
Chiarelli N +5 more
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Independent point-set dominating sets in graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 In this paper, we study graphs which possess an independent point-set dominating set (in short, ipsd-set). We call such a graph as an ipsd-graph. We first provide general structural characterization of separable ipsd-graphs and thereafter, in our quest ...
Purnima Gupta, Alka Goyal, Ranjana Jain
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Maximum independent sets of commuting and noninterfering inversions [PDF]
BMC Bioinformatics, 2009 Background Given three signed permutations, an inversion median is a fourth permutation that minimizes the sum of the pairwise inversion distances between it and the three others. This problem is NP-hard as well as hard to approximate.
Moret Bernard ME +3 more
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n-Rooks and n-queens problem on planar and modular chessboards with hexagonal cells [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 We show the existence of solutions to the n-rooks problem and n-queens problem on chessboards with hexagonal cells, problems equivalent to certain three and six direction riders on ordinary chessboards. Translating the problems into graph theory problems,
Eduard C. Taganap, Rainier D. Almuete
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On the convexity of independent set games [PDF]
Discrete Applied Mathematics, 2021 Independent set games are cooperative games defined on graphs, where players are edges and the value of a coalition is the maximum cardinality of independent sets in the subgraph defined by the coalition. In this paper, we investigate the convexity of independent set games, as convex games possess many nice properties both economically and ...
Qizhi Fang, Yuanxi Wang, Han Xiao 0003
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On the Independent Set Sequence of a Tree [PDF]
The Electronic Journal of Combinatorics, 2021 Alavi, Malde, Schwenk and Erdős asked whether the independent set sequence of every tree is unimodal. Here we make some observations about this question. We show that for the uniformly random (labelled) tree, asymptotically almost surely (a.a.s.) the initial approximately 49.5% of the sequence is increasing while the terminal approximately 38.8% is ...
Abdul Basit 0001, David J. Galvin
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Entropy, Graph Homomorphisms, and Dissociation Sets
Entropy, 2023 Given two graphs G and H, the mapping of f:V(G)→V(H) is called a graph homomorphism from G to H if it maps the adjacent vertices of G to the adjacent vertices of H.
Ziyuan Wang, Jianhua Tu, Rongling Lang
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