邻域并与[a,b]-k-对等图

Neighborhood Union for [a,b]-k-uniform Graphs

设G是一个n阶图,1≤a<b及b≥k≥0是整数,本文证明了若n≥2(a+b)(a+bb-1)+2k,图G的最小度δ(G)≥a+k,且NG(x)∪NG(y)≥ana++2bk,则G是[a,b]-k-对等图,推广了已有的结果。

Let G be a graph of order n, and let k, a and b be integers such that 1 ≤a 〈b,0≤k≤b and n≥ 2（a＋b）（a＋b-1）＋2k/b.Then it is proved that G is an [ a, b ]-k-uniform graph if the minimum degree δ（G）a＋k,and ｜NG（x）∪NG（y）｜≥an＋2k/a＋b .This result is an extension of some results.