# Search results for: Xueliang Li

Applied Mathematics Letters > 2009 > 22 > 10 > 1525-1528

Discrete Mathematics > 2009 > 309 > 10 > 3370-3380

Discrete Mathematics > 2009 > 309 > 8 > 2575-2578

Applied Mathematics Letters > 2009 > 22 > 10 > 1525-1528

Given a graph G and a subgraph H of G, let rb(G,H) be the minimum number r for which any edge-coloring of G with r colors has a rainbow subgraph H. The number rb(G,H) is called the rainbow number of H with respect to G. Denote as mK2 a matching of size m and as Bn,k the set of all the k-regular bipartite graphs with bipartition (X,Y) such that ∣X∣=∣Y∣=n and k≤n. Let k,m,n be given positive integers,...

Discrete Mathematics > 2009 > 309 > 10 > 3370-3380

For a given graph H and a positive n, the rainbow number of H, denoted by rb(n,H), is the minimum integer k so that in any edge-coloring of Kn with k colors there is a copy of H whose edges have distinct colors. In 2004, Schiermeyer determined rb(n,kK2) for all n≥3k+3. The case for smaller values of n (namely, n∈[2k,3k+2]) remained generally open. In this paper we extend Schiermeyer’s result to all...

Discrete Mathematics > 2009 > 309 > 8 > 2575-2578

Given two graphs G and H, let f(G,H) denote the maximum number c for which there is a way to color the edges of G with c colors such that every subgraph H of G has at least two edges of the same color. Equivalently, any edge-coloring of G with at least rb(G,H)=f(G,H)+1 colors contains a rainbow copy of H, where a rainbow subgraph of an edge-colored graph is such that no two edges of it have the same...