Discussiones Mathematicae Graph Theory 31(2) (2011) 387-395
doi: 10.7151/dmgt.1553

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Bounds for the Rainbow Connection Number of Graphs

Ingo Schiermeyer

Institut für Diskrete Mathematik und Algebra
Technische Universität Bergakademie Freiberg
09596 Freiberg Germany


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 show some new bounds for the rainbow connection number of graphs depending on the minimum degree and other graph parameters. Moreover, we discuss sharpness of some of these bounds.

Keywords: rainbow colouring, rainbow connectivity, extremal problem

2010 Mathematics Subject Classification: 05C35, 05C15.


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Received 5 January 2010
Revised 14 January 2011
Accepted 17 January 2011