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Discussiones Mathematicae Graph Theory 31(2) (2011)
313-320
DOI: https://doi.org/10.7151/dmgt.1547
GRAPHS WITH RAINBOW CONNECTION NUMBER TWO
| Arnfried Kemnitz
Computational Mathematics | Ingo Schiermeyer
Institut für Diskrete Mathematik und Algebra |
Abstract
An edge-coloured graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colours. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colours that are needed in order to make G rainbow connected. In this paper we prove that rc(G) = 2 for every connected graph G of order n and size m, where ((n−1) || 2)+1 ≤ m ≤ (n || 2) −1. We also characterize graphs with rainbow connection number two and large clique number.Keywords: edge colouring, rainbow colouring, rainbow connection.
2010 Mathematics Subject Classification: 05C15, 05C35.
References
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Received 4 December 2009
Revised 12 May 2010
Accepted 12 May 2010
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