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.
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 | |
| State | Published - 2002 |
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics