We prove the following best possible result. Let k 2 be an integer and G be a graph of order n with minimum degree at least k. Assume n 8k - 16 for even n and n 6k-13 for odd n...
Alon and Yuster [4] have proven that if a fixed graph K on g vertices is (h + 1)-colorable, then any graph G with n vertices and minimum degree at least h h+1 n contains at least ...
We prove that for every c > 0 there exists a constant K = K(c) such that every graph G with n vertices and minimum degree at least cn contains a cycle of length t for every even...
Let k be an integer and M be a closed 2-manifold with Euler characteristic (M) 0. We prove that each polyhedral map G on M with minimum degree and large number of vertices conta...
A generalized p-cycle is a digraph whose set of vertices can be partitioned into p parts that are cyclically ordered in such a way that the vertices in one part are adjacent only ...
It is proved in this paper that every bipartite graphic sequence with the minimum degree 2 has a realization that admits a nowhere-zero 4-flow. This result implies a conjecture ...
Let G be a simple graph with order n and minimum degree at least two. In this paper, we prove that if every odd branch-bond in G has an edge-branch, then its line graph has a 2-fa...
Jun Fujisawa, Liming Xiong, Kiyoshi Yoshimoto, She...
In a graph G, a vertex dominates itself and its neighbors. A subset S ⊆ V (G) is an m-tuple dominating set if S dominates every vertex of G at least m times, and an m-dominating...
Let H be a multigraph and G a graph containing a subgraph isomorphic to a subdivision of H, with S ⊂ V (G) (the ground set) the image of V (H) under the isomorphism. We consider...