论文信息 - On the number of vertices belonging to all maximum stable sets of a graph

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

Let us denote by (G) the size of a maximum stable set, and by (G) the size of a maximum matching of a graph G, and let (G) be the number of vertices which belong to all maximum stable sets. We shall show that (G)¿ 1+ (G)− (G) holds for any connected graph, whenever (G)¿ (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, (G)¿ 0 can be recognized in polynomial time whenever (G)¡ |V (G)|=3, and on the other hand determining whether (G)¿k is, in general, NP-complete for any @xed k¿ 0. ? 2002 Elsevier Science B.V. All rights reserved.

Endre Boros | Martin Charles Golumbic | Vadim E. Levit | M. Golumbic | E. Boros

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