Very well covered graphs
نویسندگان
چکیده
منابع مشابه
Very well-covered graphs and the unimodality conjecture
If sk denotes the number of stable sets of cardinality k in the graph G,
متن کاملVery well-covered graphs with log-concave independence polynomials
If sk equals the number of stable sets of cardinality k in the graph G, then I(G; x) = α(G) ∑ k=0 skx k is the independence polynomial of G (Gutman and Harary, 1983). Alavi, Malde, Schwenk and Erdös (1987) conjectured that I(G; x) is unimodal whenever G is a forest, while Brown, Dilcher and Nowakowski (2000) conjectured that I(G; x) is unimodal for any well-covered graph G. Michael and Traves (...
متن کاملWell-covered circulant graphs
A graph is well-covered if every independent set can be extended to a maximum independent set. We show that it is co-NP-complete to determine whether an arbitrary graph is well-covered, even when restricted to the family of circulant graphs. Despite the intractability of characterizing the complete set of well-covered circulant graphs, we apply the theory of independence polynomials to show tha...
متن کاملRecursively decomposable well-covered graphs
We give an alternative characterization for well-covered graphs and restrict this to a characterization for very well covered graphs. We state the conditions under which the intersection of a pair of maximal independent sets of a well-covered graph is maximal and use this result to deene and characterize two recursively decomposable sub-classes of well-covered graphs, one properly containing th...
متن کاملWell-covered graphs and factors
A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality . 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 spa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1982
ISSN: 0012-365X
DOI: 10.1016/0012-365x(82)90215-1