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

Martin Golumbic, Endre Boros, Vadim E. Levit

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)17-25
Number of pages9
JournalDiscrete Applied Mathematics
Volume124
Issue number1-3
DOIs
StatePublished - 2002

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Fingerprint

Dive into the research topics of 'On the number of vertices belonging to all maximum stable sets of a graph'. Together they form a unique fingerprint.

Cite this