Results 11 to 20 of about 2,644,664 (312)
On the independent set interdiction problem [PDF]
Electronic Journal of Graph Theory and Applications, 2015 The purpose of the independent set interdiction problem in the weighted graph $G$ is to determine a set of vertices $R^*$ such that the weight of the maximum independent set in $G-R^*$ is minimized.
Gholam Hassan Shirdel, Nasrin Kahkeshani
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Extremal Independent Set Reconfiguration
The Electronic Journal of Combinatorics, 2023 The independent set reconfiguration problem asks whether one can transform one given independent set of a graph into another, by changing vertices one by one in such a way the intermediate sets remain independent. Extremal problems on independent sets are widely studied: for example, it is well known that an $n$-vertex graph has at most $3^{n/3 ...
Bousquet, Nicolas +3 more
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Engineering Science and Technology, an International JournalIn this study, a method has been developed for solving the maximum independent set problem, which is one of the significant problems in graph theory. The maximum independent set problem is NP-hard for all types of graphs.
Furkan Öztemiz
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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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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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1-Extendability of Independent Sets
Algorithmica, 2022 Abstract In the 70s, Berge introduced 1-extendable graphs (also called B-graphs), which are graphs where every vertex belongs to a maximum independent set. Motivated by an application in the design of wireless networks, we study the computational complexity of 1-extendability, the problem of deciding whether a graph is 1-extendable.
Pierre Bergé +3 more
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On independent sets in hypergraphs [PDF]
Random Structures & Algorithms, 2012 AbstractThe independence number of a hypergraph H is the size of a largest set of vertices containing no edge of H. In this paper, we prove that if Hn is an n‐vertex ‐uniform hypergraph in which every r‐element set is contained in at most d edges, where , then urn:x-wiley::media:rsa20453:rsa20453-math-0004 where satisfies as .
Alexandr V. Kostochka +2 more
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Stability for Maximal Independent Sets [PDF]
The Electronic Journal of Combinatorics, 2020 Answering questions of Y. Rabinovich, we prove "stability" versions of upper bounds on maximal independent set counts in graphs under various restrictions. Roughly these say that being close to the maximum implies existence of a large induced matching or triangle matching (depending on assumptions).
Jeff Kahn 0001, Jinyoung Park 0002
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Counting Independent Sets in Hypergraphs [PDF]
Combinatorics, Probability and Computing, 2014 Let G be a triangle-free graph with n vertices and average degree t. We show that G contains at least ${\exp\biggl({1-n^{-1/12})\frac{1}{2}\frac{n}{t}\ln t} \biggl(\frac{1}{2}\ln t-1\biggr)\biggr)}$ independent sets. This improves a recent result of the first and third authors [8]. In particular, it implies that as n → ∞, every triangle-free graph on n
Jeff Cooper, Kunal Dutta, Dhruv Mubayi
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