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arXiv · 1701.03780

Generalised Majority Colourings of Digraphs

António Girão·Teeradej Kittipassorn·Kamil Popielarz
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Abstract

The purpose of this note is to draw attention to problems related to a concept called majority colouring recently studied by Kreutzer, Oum, Seymour, van der Zypen and Wood. They raised a problem of determining, for a natural number $k$, the smallest number $m=m(k)$ such that every digraph can be coloured with $m$ colours where each vertex has the same colour as at most $1/k$ proportion of its out-neighbours. We show that $m(k)\in\{2k-1,2k\}$. We also prove a result supporting the conjecture that $m(2)=3$. Moreover, we prove similar results for a more general concept called majority choosability.

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António Girão, Teeradej Kittipassorn, Kamil Popielarz. 2017-01-13. Generalised Majority Colourings of Digraphs. https://doi.org/10.1017/s096354831700044x

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