Some Remarks on Rainbow Connectivity

Nina Kamčev; Michael Krivelevich; Benny Sudakov

doi:10.1016/j.endm.2015.06.019

Some Remarks on Rainbow Connectivity

Nina Kamčev, Michael Krivelevich, Benny Sudakov

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	123-131
Number of pages	9
Journal	Electronic Notes in Discrete Mathematics
Volume	49
DOIs	https://doi.org/10.1016/j.endm.2015.06.019
State	Published - Nov 2015

Keywords

Diameter
Rainbow connectivity
Random regular graph

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.endm.2015.06.019

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title = "Some Remarks on Rainbow Connectivity",

abstract = "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.",

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AB - 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.

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KW - Rainbow connectivity

KW - Random regular graph

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DO - 10.1016/j.endm.2015.06.019

M3 - مقالة

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SP - 123

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JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -

Some Remarks on Rainbow Connectivity

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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