The Sufficient Conditions for the Existence of Fractional Fa ctors Graphs
Hanyuan Deng · Hu'nan Shifan Daxue xuebao. Ziran kexue ban · 2003
Fractional graph theory is a new research subject in gra ph theory. Some results concerning fractional matching, fractional coloring etc have been achieved.Given a graph G=(V,E), letf:V→Z, g:V→Z, and h:Ebe three functions. We call G h fractional (g,f)-factor of G if G h＝(V,E h), where E h＝｛e∈E｜h(e)≠0｝, and g(x)≤∑x∈eh(e)≤f(x) 〓for al l x∈V(G), where x∈e denotes that e is an incident edge with vertex x. In this article, we give two new sufficient conditions for a graph which has a fractional (g,f)-factor.