Some Remarks on Rainbow Connectivity

Nina Kamčev, Michael Krivelevich, Benny Sudakov

Research output: Contribution to journalArticleOtherpeer-review


An edge- (vertex-) coloured graph is rainbow connected if there is a rainbow path between any two vertices, i.e. a path all of whose edges (internal vertices) carry distinct colours. Rainbow edge (vertex) connectivity of a graph G is the smallest number of colours needed for a rainbow edge (vertex) colouring of G. In this paper we propose a very simple approach to studying rainbow connectivity in graphs. Using this idea, we give a unified proof of several new and known results, focusing on random regular graphs.

Original languageEnglish
Pages (from-to)123-131
Number of pages9
JournalElectronic Notes in Discrete Mathematics
Publication statusPublished - 1 Nov 2015
Externally publishedYes


  • Diameter
  • Rainbow connectivity
  • Random regular graph

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