Let G be a graph and k≥2 a positive integer. Let h ： E（G）→[0, 1] be a function. If e∑eЭxh（e） = k holds for each x∈V（G）, then we call G[Fh ] a fractional k-factor of G with indicator function h where Fh ={e...Let G be a graph and k≥2 a positive integer. Let h ： E（G）→[0, 1] be a function. If e∑eЭxh（e） = k holds for each x∈V（G）, then we call G[Fh ] a fractional k-factor of G with indicator function h where Fh ={e∈E（G） ： h（e） 〉 0}. A graph G is fractional independent-set-deletable k-factor-critical（in short, fractional ID-k-factor-critical）, if G-I has a fractional k-factor for every independent set I of G. In this paper, we prove that if n≥9 k-14 and for any subset X？V（G） we have NG（X） = V（G） if ｜X｜ ≥ kn/（3k-1）; or ｜NG（X）3 k-1/k｜ ≥｜X｜if｜X｜〈 kn/（3k-1）,then G is fractional ID-k-factor-critical.展开更多
Let G be a graph, and k a positive integer. A graph G is fractional independent-set-deletable k-factor-critical(in short, fractional ID-k-factor-critical) if G-I has a fractional k-factor for every independent set I o...Let G be a graph, and k a positive integer. A graph G is fractional independent-set-deletable k-factor-critical(in short, fractional ID-k-factor-critical) if G-I has a fractional k-factor for every independent set I of G. In this paper, we present a sufficient condition for a graph to be fractional ID-k-factor-critical,depending on the minimum degree and the neighborhoods of independent sets. Furthermore, it is shown that this result in this paper is best possible in some sense.展开更多
基金sponsored by the National Natural Science Foundation of China(Grant No.11371009,11501256,61503160)the National Social Science Foundation of China(Grant No.11BGL039)+1 种基金Six Big Talent Peak of Jiangsu Province(Grant No.JY–022)333 Project of Jiangsu Province
文摘Let G be a graph and k≥2 a positive integer. Let h ： E（G）→[0, 1] be a function. If e∑eЭxh（e） = k holds for each x∈V（G）, then we call G[Fh ] a fractional k-factor of G with indicator function h where Fh ={e∈E（G） ： h（e） 〉 0}. A graph G is fractional independent-set-deletable k-factor-critical（in short, fractional ID-k-factor-critical）, if G-I has a fractional k-factor for every independent set I of G. In this paper, we prove that if n≥9 k-14 and for any subset X？V（G） we have NG（X） = V（G） if ｜X｜ ≥ kn/（3k-1）; or ｜NG（X）3 k-1/k｜ ≥｜X｜if｜X｜〈 kn/（3k-1）,then G is fractional ID-k-factor-critical.
基金supported by the National Natural Science Foundation of China(Grant No.11371009,11501256,61503160)Six Big Talent Peak of Jiangsu Province(Grant No.JY–022)+3 种基金333 Project of Jiangsu Provincethe National Social Science Foundation of China(Grant No.14AGL001)the Natural Science Foundation of Xinjiang Province of China(Grant No.2015211A003)the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province(Grant No.14KJD110002)
文摘Let G be a graph, and k a positive integer. A graph G is fractional independent-set-deletable k-factor-critical(in short, fractional ID-k-factor-critical) if G-I has a fractional k-factor for every independent set I of G. In this paper, we present a sufficient condition for a graph to be fractional ID-k-factor-critical,depending on the minimum degree and the neighborhoods of independent sets. Furthermore, it is shown that this result in this paper is best possible in some sense.
