A MINIMUM DEGREE CONDITION FOR FRACTIONAL ID-[a,b]-FACTOR-CRITICAL GRAPHS
نویسندگان
چکیده
منابع مشابه
A degree condition for graphs to be fractional ID-[a, b]-factor-critical
Let G be a graph of sufficiently large order n, and let a and b be integers with 1 ≤ a ≤ b. Let h : E(G) → [0, 1] be a function. If a ≤ ∑x∈e h(e) ≤ b holds for any x ∈ V (G), then G[Fh] is called a fractional [a, b]-factor of G with indicator function h, where Fh = {e ∈ E(G) | h(e) > 0}. A graph G is fractional independent-set-deletable [a, b]-factor-critical (simply, fractional ID-[a, b]-facto...
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We say that a simple graph G is fractional independent-set-deletable k-factor-critical, shortly, fractional ID-k-factor-critical, if G− I has a fractional k-factor for every independent set I of G. Some sufficient conditions for a graph to be fractional ID-k-factor-critical are studied in this paper. Furthermore, we show that the result is best possible in some sense. 2010 Mathematics Subject C...
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A graphG is fractional ID-[a, b]-factor-critical ifG−I includes a fractional [a, b]-factor for every independent set I of G. In this paper, it is proved that if α(G) ≤ 4b(δ(G)−a+1) (a+1)2+4b , then G is fractional ID-[a, b]-factor-critical. Furthermore, it is shown that the result is best possible in some sense.
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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...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2012
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972711003467