Elsevier

Discrete Mathematics

Volume 310, Issue 20, 28 October 2010, Pages 2662-2665
Discrete Mathematics

Hadwiger numbers and over-dominating colourings

To Carsten Thomassen on his 60th birthday
https://doi.org/10.1016/j.disc.2010.03.024Get rights and content
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Abstract

Motivated by Hadwiger’s conjecture, we say that a colouring of a graph is over-dominating if every vertex is joined to a vertex of each other colour and if, for each pair of colour classes C1 and C2, either C1 has a vertex adjacent to all vertices in C2 or C2 has a vertex adjacent to all vertices in C1.

We show that a graph that has an over-dominating colouring with k colours has a complete minor of order at least 2k/3 and that this bound is essentially best possible.

Keywords

Hadwiger minor over-dominating

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