Showing papers by "Xueliang Li published in 2004"
TL;DR: A su5cient and necessary condition for a graph G with p vertices and � (G) ?
11 citations
TL;DR: The problem on how many removable edges there are in a cycle of a 4-connected graph is investigated, and examples are given to show that the results are in some sense the best possible.
5 citations
TL;DR: For graphs G and G^' with minimum degree at least k, when k>=4, it was shown in this paper that any isomorphism from the P"k-graph of G onto G can be induced by a (vertex-)isomorphism of G on G^''.
5 citations
01 Jan 2004
TL;DR: Examples are given to show that a conjecture on k-walks of graphs, due to B. Jackson and N.C. Wormald, is false and a maximum degree condition for the existence of k-Walks and k-trees in 2connected graphs is given.
Abstract: In this paper we give examples to show that a conjecture on k-walks of graphs, due to B. Jackson and N.C. Wormald, is false. We also give a maximum degree condition for the existence of k-walks and k-trees in 2connected graphs.
5 citations
TL;DR: A useful inequality on the minimum real roots of the adjoint polynomials of the complete graphs is established and used to investigate the chromatic uniqueness of certain complete multipartite graphs.
Abstract: In this paper, we first establish a useful inequality on the minimum real roots of the adjoint polynomials of the complete graphs By using it, we investigate the chromatic uniqueness of certain complete multipartite graphs An unsolved problem (ie, Problem 11), posed by Koh and Teo in Graph and Combin 6(1990) 259–285, is completely solved by giving it a positive answer Moreover, many existing results on the chromatic uniqueness of complete multipartite graphs are generalized
4 citations
TL;DR: It is shown that for a 4-connected graph G of minimum degree at least 5 or girth at least 4, any edge of G is removable or contractible.
Abstract: Let G be a 4-connected graph. For an edge e of G, we do the following operations on G: first, delete the edge e from G, resulting the graph G−e; second, for all vertices x of degree 3 in G−e, delete x from G−e and then completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we use single edges to replace them. The final resultant graph is denoted by G⊖e. If G⊖e is 4-connected, then e is called a removable edge of G. In this paper we obtain some results on removable edges in a longest cycle of a 4-connected graph G. We also show that for a 4-connected graph G of minimum degree at least 5 or girth at least 4, any edge of G is removable or contractible.
1 citations