A characterization of well covered graphs of girth 5 or greater
Journal of Combinatorial Theory Series B
Well-covered graphs and extendability
Discrete Mathematics
A characterization of well-covered graphs that contain neither 4- nor 5-cycles
Journal of Graph Theory
Recursively decomposable well-covered graphs
Discrete Mathematics
Regular factors of simple regular graphs and factor-spectra
Discrete Mathematics
Independent domination and matchings in graphs
Discrete Mathematics
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A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality @a. 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 F"G, i.e. a spanning subgraph such that each component is 1-regular or 2-regular. Here, we characterize all well-covered graphs G satisfying @a(G)=@a(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 @a=(n-1)/2, and in particular all very well-covered graphs.