TIGHT TOUGHNESS CONDITION FOR FRACTIONAL (g, f, n)-CRITICAL GRAPHS
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چکیده
All graphs considered in this paper are finite, loopless, and without multiple edges. The notation and terminology used but undefined in this paper can be found in [2]. Let G be a graph with the vertex set V (G) and the edge set E(G). For a vertex x ∈ V (G), we use dG(x) and NG(x) to denote the degree and the neighborhood of x in G, respectively. Let δ(G) denote the minimum degree of G. For any S ⊆ V (G), the subgraph of G induced by S is denoted by G[S]. Suppose that g and f are two integer-valued functions on V (G) such that 0 ≤ g(x) ≤ f(x) for all x ∈ V (G). A spanning subgraph F of G is called a (g, f)-factor if g(x) ≤ dF (x) ≤ f(x) for each x ∈ V (G). A fractional (g, f)factor is a function h that assigns to each edge of a graph G a number in [0,1] so that for each vertex x we have g(x) ≤ ∑
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تاریخ انتشار 2013