均衡二分图中哈密顿[k,k+1]-因子的存在条件

The Existence Condition of Hamiltonian [k,k+1]-factor in Balanced Bipartite Graph

设k≥2是一个正整数,若G是顶点数n≥8k-12的均衡二分图且是(n/4+1)-临界的,则对G的任一给定的哈密顿圈C,G都有一个[k,k+1]-因子包含C.该结论改进了现有的一些有关哈密顿[k,k+1]-因子存在性的结果.

Let k≥2 be a positive integer, if G is a balanced bipartite graph with vertex number n≥8k - 12 and （n/4 ＋ 1 ） - critical, then for any given Hamihonian cycle C, G has a [ k, k ＋ 1 ] - factor containing C. This result is an improvement for some results about the existence of Hamiltonian [ k, k ＋ 1 ] - factor.