Abstract
A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality α. Plummer defined a graph to be well-covered, if every independent set is contained in a maximum independent set of G. Every well-covered graph G without isolated vertices has a perfect [1,2]-factor F_G, i.e. a spanning subgraph such that each component is 1-regular og 2-regular. Here, we characterize all well-covered graphs G satisfying α(G)=α(F_G) for some perfect [1,2]-factor F_G. This class contains all well-covered graphs G without isolated vertices of order n with α ≥ (n - 1)/2, and in particular all very well-covered graphs.
Udgivelsesdato: JUN 1
Udgivelsesdato: JUN 1
Originalsprog | Engelsk |
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Tidsskrift | Discrete Applied Mathematics |
Vol/bind | 154 |
Udgave nummer | 9 |
Sider (fra-til) | 1416-1428 |
Antal sider | 13 |
ISSN | 0166-218X |
Status | Udgivet - 2006 |