Bounds for the rainbow connection number of graphs | Zendy

Ingo Schiermeyer | Zendy

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Bounds for the rainbow connection number of graphs

Author(s) -

Ingo Schiermeyer

Publication year - 2011

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1553

Subject(s) - mathematics , combinatorics , connection (principal bundle) , rainbow , domination analysis , discrete mathematics , graph , geometry , vertex (graph theory) , physics , quantum mechanics

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 makeG rainbowconnected. 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.

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