Well-covered graphs and factors

Authors:
Bert Randerath;Preben Dahl Vestergaard
Affiliations:
Institut für Informatik, Universität zu Köln, Köln, Germany;Mathematics Department, Aalborg University, Aalborg Ø, Denmark
Venue:
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
Year:
2006

Citing 6
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Abstract

A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality α. Plummer [Some covering concepts in graphs, J. Combin. Theory 8 (1970) 91-98] 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 FG, i.e. a spanning subgraph such that each component is 1-regular or 2-regular. Here, we characterize all well-covered graphs G satisfying α(G) = α(FG) for some perfect [1,2]-factor FG. 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.