On Duality between Local Maximum Stable Sets of a Graph and its Line-Graph - Mathematics > CombinatoricsReport as inadecuate




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Abstract: G is a Koenig-Egervary graph provided alphaG+ muG=|VG|, where muG isthe size of a maximum matching and alphaG is the cardinality of a maximumstable set. S is a local maximum stable set of G if S is a maximum stable setof the closed neighborhood of S. Nemhauser and Trotter Jr. proved that anylocal maximum stable set is a subset of a maximum stable set of G. In thispaper we demonstrate that if S is a local maximum stable set, the subgraph Hinduced by the closed neighborhood of S is a Koenig-Egervary graph, and M is amaximum matching in H, then M is a local maximum stable set in the line graphof G.



Author: Vadim E. Levit, Eugen Mandrescu

Source: https://arxiv.org/



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