Some Remarks on Rainbow Connectivity
Nina Kam\v{c}ev, Michael Krivelevich, Benny Sudakov
TL;DR
This paper introduces a simple approach to studying rainbow connectivity in graphs, providing unified proofs of existing results and new insights into the minimum number of colours needed for rainbow connectivity.
Contribution
It offers a unified proof technique for known results and presents new findings in the study of rainbow connectivity in graphs.
Findings
Unified proof method for rainbow connectivity results
New bounds on the number of colours needed for rainbow connectivity
Simplified approach to studying 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 is the smallest number of colours needed for a rainbow edge (vertex) colouring of . 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 known results, as well as some new ones.
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