Well-covered graphs and factors

Bert Randerath, Preben D. Vestergaard

Research output: Contribution to journalJournal articleResearchpeer-review

4 Citations (Scopus)


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.
Original languageEnglish
JournalDiscrete Applied Mathematics
Issue number9
Pages (from-to)1416-1428
Number of pages13
Publication statusPublished - 2006

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