摘要
1978年,Caccetta和Hggkvist提出如下至今仍未解决的猜想:最小出度不小于r的n阶有向图含有长度不大于[n/r]的有向圈.本文证明了:当α≥0.28724时,最小出度至少αn的n阶有向图含有长度不超过4的有向圈.
In 1978, Caccetta and Haggkvist made an open conjecture: Any digraph on n vertices with minimum outdegree at least r contains a directed cycle of length at most [n/r]. We prove that if a ≥ 0.28724, then any digraph on n vertices with minimum outdegree at least an contains a directed cycle of length at most 4.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
2013年第4期479-486,共8页
Acta Mathematica Sinica:Chinese Series
基金
国家自然科学基金资助项目(11071233)