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Rainbow Connection Number and Connectivity

Li, Xueliang and Liu, Sujuan and Chandran, Sunil L and Mathew, Rogers and Rajendraprasad, Deepak (2012) Rainbow Connection Number and Connectivity. In: Electronic Journal of Combinatorics, 19 (1).

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Abstract

The rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges, so that every pair of vertices is connected by at least one path in which no two edges are colored the same. Our main result is that rc(G) <= inverted right perpendicularn/2inverted left perpendicular for any 2-connected graph with at least three vertices. We conjecture that rc(G) <= n/kappa + C for a kappa-connected graph G of order n, where C is a constant, and prove the conjecture for certain classes of graphs. We also prove that rc(G) < (2 + epsilon)n/kappa + 23/epsilon(2) for any epsilon > 0.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Department of Mathematics, University of Pennsylvania.
Keywords: rainbow coloring;rainbow connection number;connectivity; 2-connected graph;ear decomposition;chordal graph;girth
Department/Centre: Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation)
Date Deposited: 13 Mar 2012 05:14
Last Modified: 13 Mar 2012 05:14
URI: http://eprints.iisc.ernet.in/id/eprint/43852

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