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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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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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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).
Kahn, Jeff, Park, Jinyoung
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Theoretical Computer Science, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Halldórsson, Magnús M. +3 more
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Combinatorics, Probability and Computing, 2012 The study of extremal problems related to independent sets in hypergraphs is a problem that has generated much interest. There are a variety of types of independent sets in hypergraphs depending on the number of vertices from an independent set allowed in an edge.
Cutler, Jonathan, Radcliffe, A. J.
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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
Cooper, J., Dutta, K., Mubayi, D.
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Beeping a maximal independent set [PDF]
Distributed Computing, 2011 arXiv admin note: substantial text overlap with arXiv:1108 ...
Afek, Yehuda +5 more
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Large Independent Sets on Random d-Regular Graphs with Fixed Degree d
Computation, 2023 The maximum independent set problem is a classic and fundamental combinatorial challenge, where the objective is to find the largest subset of vertices in a graph such that no two vertices are adjacent.
Raffaele Marino, Scott Kirkpatrick
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European Journal of Combinatorics, 2014 Yannakakis' Clique versus Independent Set problem (CL-IS) in communication complexity asks for the minimum number of cuts separating cliques from stable sets in a graph, called CS-separator. Yannakakis provides a quasi-polynomial CS-separator, i.e. of size $O(n^{\log n})$, and addresses the problem of finding a polynomial CS-separator. This question is
Bousquet, Nicolas +2 more
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Critical sets, crowns and local maximum independent sets [PDF]
Journal of Global Optimization, 2021 19 pages, 11 ...
Vadim E. Levit, Eugen Mandrescu
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