On rainbow-k-connectivity of random graphs

Authors:
Jing He;Hongyu Liang
Affiliations:
Institute for Interdisciplinary Information Sciences, FIT Building 4-609, Tsinghua University, Beijing 100084, China;Institute for Interdisciplinary Information Sciences, FIT Building 4-609, Tsinghua University, Beijing 100084, China
Venue:
Information Processing Letters
Year:
2012

Citing 4
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Abstract

A path in an edge-colored graph is called a rainbow path if the edges on it have distinct colors. For k=1, the rainbow-k-connectivity of a graph G, denoted by rc"k(G), is the minimum number of colors required to color the edges of G in such a way that every two distinct vertices are connected by at least k internally vertex-disjoint rainbow paths. In this paper, we study rainbow-k-connectivity in the setting of random graphs. We show that for every fixed integer d=2 and every k=