@inproceedings{88c94ade3d0a49029027cf4c42c9b206,
title = "The Binding Number of a Digraph",
abstract = "Caccetta-H{\"a}ggkvist's Conjecture discusses the relation between the girth g(D) of a digraph D and the minimum outdegree δ +(D) of D. The special case when g(D) = 3 has lately attracted wide attention. For an undirected graph G, the binding number is a sufficient condition for G to have a triangle (cycle with length 3). In this paper we generalize the concept of binding numbers to digraphs and give some corresponding results. In particular, the value range of binding numbers is given, and the existence of digraphs with a given binding number is confirmed. By using the binding number of a digraph we give a condition that guarantees the existence of a directed triangle in the digraph. The relationship between binding number and connectivity is also discussed.",
keywords = "Binding number, Caccetta-H{\"a}ggkvist Conjecture, Directed graph, Girth",
author = "Genjiu Xu and Xueliang Li and Shenggui Zhang",
year = "2007",
doi = "10.1007/978-3-540-70666-3_24",
language = "英语",
isbn = "3540706658",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "221--227",
booktitle = "Discrete Geometry, Combinatorics and Graph Theory 7th China-Japan Conference, CJCDGCGT 2005, Tianjin, China, November 18-20, 2005, Xi'an, China, November 22-24, 2005, Revised Selected Papers",
note = "7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005 ; Conference date: 22-11-2005 Through 24-11-2005",
}