On Well-Covered, Vertex Decomposable and Cohen-Macaulay Graphs
نویسندگان
چکیده
منابع مشابه
On Well-Covered, Vertex Decomposable and Cohen-Macaulay Graphs
Let G = (V,E) be a graph. If G is a König graph or if G is a graph without 3-cycles and 5-cycles, we prove that the following conditions are equivalent: ∆G is pure shellable, R/I∆ is Cohen-Macaulay, G is an unmixed vertex decomposable graph and G is well-covered with a perfect matching of König type e1, . . . , eg without 4-cycles with two ei’s. Furthermore, we study vertex decomposable and she...
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We call a vertex x of a graph G = (V,E) a codominated vertex if NG[y] ⊆ NG[x] for some vertex y ∈ V \{x}, and a graph G is called codismantlable if either it is an edgeless graph or it contains a codominated vertex x such that G − x is codismantlable. We show that (C4, C5)-free vertex-decomposable graphs are codismantlable, and prove that if G is a (C4, C5, C7)-free well-covered graph, then ver...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2016
ISSN: 1077-8926
DOI: 10.37236/5874