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arXiv · 2203.10402

Odd colourings, conflict-free colourings and strong colouring numbers

Robert Hickingbotham
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Abstract

The odd chromatic number and the conflict-free chromatic number are new graph parameters introduced by Petru\v{s}evski and \v{S}krekovski [2021] and Fabrici, Lu\v{z}ar, Rindo\v{s}ov\'a and Sot\'ak [2022] respectively. In this note, we show that graphs with bounded $2$-strong colouring number have bounded odd chromatic number and bounded conflict-free chromatic number. This implies that graph classes with bounded expansion have bounded odd chromatic number and bounded conflict-free chromatic number. Moreover, it follows by known results that the odd chromatic number and the conflict-free chromatic number of $k$-planar graphs is $O(k)$ which improves a recent result of Dujmovi\'{c}, Morin and Odak [2022].

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Robert Hickingbotham. 2022-03-19. Odd colourings, conflict-free colourings and strong colouring numbers. https://arxiv.org/abs/2203.10402

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