Results 51 to 60 of about 13,294,177 (308)
The Hilton-Spencer Cycle Theorems Via Katona’s Shadow Intersection Theorem
Discussiones Mathematicae Graph Theory, 2023 A family 𝒜 of sets is said to be intersecting if every two sets in 𝒜 intersect. An intersecting family is said to be trivial if its sets have a common element.
Borg Peter, Feghali Carl
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On the Independence Number of Cayley Digraphs of Clifford Semigroups
Mathematics, 2023 Let S be a Clifford semigroup and A a subset of S. We write Cay(S,A) for the Cayley digraph of a Clifford semigroup S relative to A. The (weak, path, weak path) independence number of a graph is the maximum cardinality of an (weakly, path, weakly path ...
Krittawit Limkul, Sayan Panma
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The Complexity of Independent Set Reconfiguration on Bipartite Graphs [PDF]
ACM-SIAM Symposium on Discrete Algorithms, 2017 We settle the complexity of the Independent Set Reconfiguration problem on bipartite graphs under all three commonly studied reconfiguration models. We show that under the token jumping or token addition/removal model, the problem is NP-complete. For the
D. Lokshtanov, A. Mouawad
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Application of an Extremal Result of Erdős and Gallai to the (n,k,t) Problem
Theory and Applications of Graphs, 2017 An extremal result about vertex covers, attributed by Hajnal to Erdős and Gallai, is applied to prove the following: If n, k, and t are integers satisfying n ≥ k ≥ t ≥ 3 and k ≤ 2t - 2, and G is a graph with the minimum number of edges among graphs on n ...
Matt Noble +3 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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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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Counting Maximal Distance-Independent Sets in Grid Graphs
Discussiones Mathematicae Graph Theory, 2013 Previous work on counting maximal independent sets for paths and certain 2-dimensional grids is extended in two directions: 3-dimensional grid graphs are included and, for some/any ℓ ∈ N, maximal distance-ℓ independent (or simply: maximal ℓ-independent ...
Euler Reinhardt +2 more
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Twin-width III: Max Independent Set, Min Dominating Set, and Coloring
International Colloquium on Automata, Languages and ProgrammingWe recently introduced the notion of twin-width, a novel graph invariant, and showed that first-order model checking can be solved in time f ( d, k ) n for n -vertex graphs given with a witness that the twin-width is at most d , called d -contraction ...
Édouard Bonnet +4 more
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Distributed Maximal Independent Set using Small Messages
ACM-SIAM Symposium on Discrete Algorithms, 2019 Maximal Independent Set (MIS) is one of the central problems in distributed graph algorithms. The celebrated works of Luby [STOC'85] and Alon, Babai, and Itai [JALG'86] provide O(log n)-round randomized distributed MIS algorithms, which work with O(log n)
M. Ghaffari
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Polynomial-time Algorithm for Maximum Weight Independent Set on P6-free Graphs [PDF]
ACM Trans. Algorithms, 2017 In the classic Maximum Weight Independent Set problem, we are given a graph G with a nonnegative weight function on its vertices, and the goal is to find an independent set in G of maximum possible weight. While the problem is NP-hard in general, we give
Andrzej Grzesik +3 more
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