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On $��^{++}$-Stable Graphs
- Publication Year :
- 2000
- Publisher :
- arXiv, 2000.
-
Abstract
- The stability number of a graph G, denoted by alpha(G), is the cardinality of a stable set of maximum size in G. A graph is well-covered if every maximal stable set has the same size. G is a Koenig-Egervary graph if its order equals alpha(G) + mu(G), where mu(G) is the cardinality of a maximum matching in G. In this paper we characterize $��^{++}$-stable graphs, namely, the graphs whose stability numbers are invariant to adding any two edges from their complements. We show that a K��nig-Egerv��ry graph is $��^{++}$-stable if and only if it has a perfect matching consisting of pendant edges and no four vertices of the graph span a cycle. As a corollary it gives necessary and sufficient conditions for $��^{++}$-stability of bipartite graphs and trees. For instance, we prove that a bipartite graph is $��^{++}$-stable if and only if it is well-covered and C4-free.<br />11 pages, 3 figures
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi...........54125555e9e6da6ee31f7f9f53631ed6
- Full Text :
- https://doi.org/10.48550/arxiv.math/0003057