supported by the National Natural Science Foundation of China(Nos.12071260,11671232)。
A tournament is an orientation of the complete graph.Tournaments form perhaps the most interesting class of digraphs and it has a great potential for application.Tournaments provide a model of the statistical techniqu...
supported by the Natural Science Young Foundation of China(No.11701349);by the Natural Science Foundation of Shanxi Province,China(No.201601D011005);by Shanxi Scholarship Council of China(2017-018)
Gutin and Rafiey(Australas J. Combin. 34(2006), 17-21) provided an example of an n-partite tournament with exactly n-m + 1 cycles of length of m for any given m with 4 ≤ m ≤ n, and posed the following question....
Supported by the National Natural Science Foundation of China(No.11731002);the Fundamental Research Funds for the Central Universities(Nos.2016JBM071,2016JBZ012)
An embedding of a digraph in an orientable surface is an embedding as the underlying graph and arcs in each region force a directed cycle. The directed genus is the minimum genus of surfaces in which the digraph can b...
In this paper we prove that if T is a regular n-partite tournament with n≥>6, then each arc of T lies on a k-cycle for k=4,5,…,n. Our result generalizes theorems due to Alspach and Guo respectively.