On X Free Covers
نویسندگان
چکیده
For an arbitrary graph G = (V,E), let X be a graphical property that can be possessed, or satisfied by the subsets of V . For example, being a clique (maximal complete subgraph), a maximal independent set, an edge, a closed neighborhood, a minimal dominating set, etc. Let CX ={A|A ⊆ V , |A| > 1, and A possesses or satisfies property X}. A set S is an X cover (or X free) if A ∩ S (or A ∩ (V − S)) is not empty for every A ∈ CX . Further, S is an X free cover when S is both X free and an X cover. Many vertex-partitioning problems can be viewed as that of finding an X free cover. In this paper, we present properties of X free covers and investigate the conditions for their existence in some special cases. This provides an underlying unification theory for these and other similar properties.
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