一类稀疏随机图的距离匹配数（英文）

On Distance Matching Number in a Class of Sparse Random Graphs

对于任意给定的正整数k,图G的距离匹配数um_k(G)是指任意两条边之间距离大于k的最大边数的集合.令G_(n,p)为经典Erds-Rényi随机图.Kang和Manggala刻画得到了当k≥2,边概率为p=c/n时稀疏Erds-Rényi随机图距离匹配数um_k(G_(n,p))的上界,其中c为足够大的常数.本文第一次利用二阶矩方法获得当k≥2时此类稀疏随机图距离匹配数的下界.

For any positive integer k, the distance matching number, denoted by umk（G）, is the largest size of a collection of edges in G such that no two edges are within distance k. Let Gn,p stand for the classic Erdos-Renyi random graph. Kang and Manggala presented an upper bound of umk（Gn,p） for k ≥ 2 and p = c/n with the constant c sufficiently large. In this paper, we firstly consider the lower bound of urnk（Gn,p） = Ω（logn） for k≥2 by the second moment method in this class of sparse random graphs.