# Search results for: Xueliang Li

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

Applied Mathematics Letters > 2009 > 22 > 3 > 320-324

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,...

Applied Mathematics Letters > 2009 > 22 > 3 > 320-324

For positive integers k and r, a conditional (k,r)-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex v of degree d(v) in G is adjacent to vertices with at least min{r,d(v)} different colors. The smallest integer k for which a graph G has a conditional (k,r)-coloring is called the rth-order conditional chromatic number, and is denoted by χr(G). It is easy to see...