On the number of vertices belonging to all maximum stable sets of a graph

Martin Golumbic; Endre Boros; Vadim E. Levit

doi:10.1016/S0166-218X(01)00327-4

On the number of vertices belonging to all maximum stable sets of a graph

Martin Golumbic
, Endre Boros
, Vadim E. Levit

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

Let us denote by α(G) the size of a maximum stable set, and by μ(G) the size of a maximum matching of a graph G, and let ξ(G) be the number of vertices which belong to all maximum stable sets. We shall show that ξ(G)⩾1+α(G)−μ(G) holds for any connected graph, whenever α(G)>μ(G). This inequality improves on related results by Hammer et al. (SIAM J. Algebraic Discrete Methods 3 (1982) 511) and by Levit and Mandrescu [(prE-print math. CO/9912047 (1999) 13pp.)].

We also prove that on one hand, ξ(G)>0 can be recognized in polynomial time whenever μ(G)k is, in general, NP-complete for any fixed k⩾0.

Original language	English
Pages (from-to)	17-25
Number of pages	9
Journal	Discrete Applied Mathematics
Volume	124
Issue number	1-3
DOIs	https://doi.org/10.1016/S0166-218X(01)00327-4
State	Published - 2002

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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AU - Boros, Endre

AU - E. Levit, Vadim

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On the number of vertices belonging to all maximum stable sets of a graph

Abstract

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