图的邻域并和连通的[k,k+1]-因子

Neighborhood Union and Connected [k,k +1]-Factors in Graphs

设G是阶为n的图.F是G的支撑子图且对所有的x∈V(G)都有k≤dF(x)≤k+1,则称F为G的[k,k+1]-因子.一个[k,k+1]-因子如果连通,则称为连通的[k,k+1]-因子.一个[k,k+1]-因子若包含一个哈密顿圈,则称为哈密顿[k,k+1]-因子.给出了图有哈密顿[k,k+1]-因子或连通的[k,k+1]-因子关于邻域并的若干新的充分条件.

Let G be a graph of order n. A spanning subgraph F of G is called a[ k, k ＋ 1 ] -factor if k ≤ dF （x） k ＋ 1 holds for each x ∈ V（G）. A [ k, k ＋ 1]-factor is called a connected [ k, k ＋ 1 ] -factor if it is connected. A [ k, k ＋ 1 ] -factor F is called a Hamilton [ k, k ＋ 1 ] -factor if F contains a Hamilton cycle. In this paper, sev- eralsufficient conditions related to neighborhood union for graphs to have connected [ k, k ＋ 1 ] -factors or Hamilton [ k, k ＋ 1 ] -factors are given.