# zbMATH — the first resource for mathematics

Hoàng-Reed conjecture holds for tournaments. (English) Zbl 1147.05038
Hoàng-Reed conjecture states that every digraph has a collection of $$m$$ circuits, where $$m$$ is the minimum out-degree of the digraph, such that these circuits have a forest-like structure. The purpose of the paper is to verify the conjecture for the class of tournaments.

##### MSC:
 05C20 Directed graphs (digraphs), tournaments 05C38 Paths and cycles
##### Keywords:
tournament; triangle structure; digraph
Full Text:
##### References:
 [1] Caccetta, L.; Häggkvist, R., On minimal digraphs with given girth, Proceedings of the ninth southeastern conference on combinatorics, graph theory, and computing, Congress. numer., XXI, 181-187, (1978) [2] Guo, Y.; Volkmann, L., Cycles in multipartite tournaments, J. combin. theory ser. B, 62, 363-366, (1994) · Zbl 0807.05034 [3] Hoàng, C.T.; Reed, B., A note on short cycles in digraphs, Discrete math., 66, 103-107, (1987) · Zbl 0626.05021 [4] B.D. Sullivan, A summary of results and problems related to the Caccetta-Häggkvist conjecture, preprint. [5] Tewes, M.; Volkmann, L., Vertex deletion and cycles in multipartite tournaments, Discrete math., 197/198, 769-779, (1999) · Zbl 0939.05046 [6] Thomassen, C., The 2-linkage problem for acyclic digraphs, Discrete math., 55, 73-87, (1985) · Zbl 0563.05027
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.