Zhang Kemin

Edge-pancyclicity of coupled graphs

The coupled graph c(G) of a plane graph G is the graph defined on the vertex set V(G)∪F(G) so that two vertices in c(G) are joined by an edge if and only if they are adjacent or incident in G. We prove that the coupled graph of a 2-connected plane graph is edge-pancyclic. However, there exists a 2-edge-connected plane graph G such that c(G) is not Hamiltonian.

Outpaths of arcs in multipartite tournaments

Ak-outpath of an arcxy in a multipartite tournament is a directed path with lengthk starting fromxy such thatx does not dominate the end vertex of the directed path. This concept is a generalization of a directed cycle. We show that ifT is an almost regularn-partite (n≥8) tournament with each partite set having at least two vertices, then every arc ofT has ak-outpath for allk, 3≤k≤n−1.

Upper bounds for ramsey numbers R(m ,n ,1) and R(m ,n, l, s) with parameter

In the paper some new upper bounds with parameters were obtained for the classical Ramsey numbers R(m, n, l) and R (m, n ,l, s). By using the upper bounds, it was proved that 72(4,4,4)≤236.