Short cycles in directed graphs
نویسندگان
چکیده
Caccetta and Haggkvist 111 conjectured that every directed graph with n vertices and minimum outdegree k contains a (directed) cycle of length at most [n/k\. (T o see that this bound cannot be improved, consider the directed graph with n cyclically arranged vertices and with edges leading from each vertex u to the first k vertices following u in the cyclic order.) Our main result (Theorem 2) is a weaker statement, in which the conjectured upper bound is raised by a constant. (For previous work on the conjecture, see 12.1 and the papers referenced there.)
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 35 شماره
صفحات -
تاریخ انتشار 1983