On local maximum stable set greedoids
نویسندگان
چکیده
منابع مشابه
Very Well-Covered Graphs of Girth at least Four and Local Maximum Stable Set Greedoids
A maximum stable set in a graph G is a stable set of maximum cardinality. S is a local maximum stable set of G, and we write S ∈ Ψ(G), if S is a maximum stable set of the subgraph induced by S ∪N(S), where N(S) is the neighborhood of S. Nemhauser and Trotter Jr. [20], proved that any S ∈ Ψ(G) is a subset of a maximum stable set of G. In [12] we have shown that the family Ψ(T ) of a forest T for...
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A maximum stable set in a graph G is a stable set of maximum cardinality. S is called a local maximum stable set of G, and we write S ∈ Ψ(G), if S is a maximum stable set of the subgraph induced by the closed neighborhood of S. A greedoid (V,F) is called a local maximum stable set greedoid if there exists a graph G = (V,E) such that F = Ψ(G). Nemhauser and Trotter Jr. [27], proved that any S ∈ ...
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A maximum stable set in a graph G is a stable set of maximum cardinality. S is a local maximum stable set of G, and we write S ∈ Ψ(G), if S is a maximum stable set of the subgraph induced by S ∪ N(S), where N(S) is the neighborhood of S. Nemhauser and Trotter Jr. [21], proved that any S ∈ Ψ(G) is a subset of a maximum stable set of G. In [14] we have shown that the family Ψ(T ) of a forest T fo...
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The stability number α(G) for a given graph G is the size of a maximum stable set in G. The Lovász theta number provides an upper bound on α(G) and can be computed in polynomial time as the optimal value of the Lovász semidefinite program. In this paper, we show that restricting the matrix variable in the Lovász semidefinite program to be rank-one and rank-two, respectively, yields a pair of co...
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We describe a new branch-and-bound algorithm for the exact solution of the maximum cardinality stable set problem. The bounding phase is based on a variation of the standard greedy algorithm for finding a colouring of a graph. Two different node-fixing heuristics are also described. Computational tests on random and structured graphs and very large graphs corresponding to 'real-life' problems s...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.04.015