Authors: Qingqiong Cai Xueliang Li Jiangli Song
Publish Date: 2015/12/30
Volume: 39, Issue: 2, Pages: 765-771
Abstract
A tree in an edgecolored graph G is said to be a rainbow tree if no two edges on the tree share the same color Given two positive integers k ell with kge 3 the kell rainbow index rx kell G of G is the minimum number of colors needed in an edgecoloring of G such that for any set S of k vertices of G there exist ell internally disjoint rainbow trees connecting S This concept was introduced by Chartrand et al and there have been very few known results about it In this paper we establish a sharp threshold function for rx kell G nple k and rx kell G nMle k respectively where G np and G nM are the usually defined random graphs
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