This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be i...This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be induced.展开更多
Let G be a graph, and g, f ： V（G）→Z＋ with g（x） 〈 f（x） for each x ∈ V（G）. We say that G admits all fractional （g, f）-factors if G contains an fractional r-factor for every r ： V（G）→ Z＋ with g（x） ...Let G be a graph, and g, f ： V（G）→Z＋ with g（x） 〈 f（x） for each x ∈ V（G）. We say that G admits all fractional （g, f）-factors if G contains an fractional r-factor for every r ： V（G）→ Z＋ with g（x） ≤ r（x） ≤ f（x） for any x ∈ V（G）. Let H be a subgraph of G. We say that G has all fractional （g, f）-factors excluding H if for every r ： V（G） → Z＋ with g（x） ≤ r（x） ≤ f（x） for all x ∈ V（G）, G has a fractional r-factor Fh such that E（H） ∩ E（Fh） = Ф, where h ： E（G） → [0, 1] is a function. In this paper, we show a characterization for the existence of all fractional （g, f）-factors excluding H and obtain two sufficient conditions for a graph to have all fractional （g, f）-factors excluding H.展开更多
基金This work is supported by NNSF of ChinaRFDP of Higher Education
文摘This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be induced.
基金supported by the National Natural Science Foundation of China(Grant No.11371009,11501256,61503160)sponsored by Six Big Talent Peak of Jiangsu Province(Grant No.JY–022)333 Project of Jiangsu Province
文摘Let G be a graph, and g, f ： V（G）→Z＋ with g（x） 〈 f（x） for each x ∈ V（G）. We say that G admits all fractional （g, f）-factors if G contains an fractional r-factor for every r ： V（G）→ Z＋ with g（x） ≤ r（x） ≤ f（x） for any x ∈ V（G）. Let H be a subgraph of G. We say that G has all fractional （g, f）-factors excluding H if for every r ： V（G） → Z＋ with g（x） ≤ r（x） ≤ f（x） for all x ∈ V（G）, G has a fractional r-factor Fh such that E（H） ∩ E（Fh） = Ф, where h ： E（G） → [0, 1] is a function. In this paper, we show a characterization for the existence of all fractional （g, f）-factors excluding H and obtain two sufficient conditions for a graph to have all fractional （g, f）-factors excluding H.
