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arXiv · 2309.05874

Cop-width, flip-width and strong colouring numbers

Robert Hickingbotham
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Abstract

Cop-width and flip-width are new families of graph parameters introduced by Toru\'nczyk (2023) that generalise treewidth, degeneracy, generalised colouring numbers, clique-width and twin-width. In this paper, we bound the cop-width and flip-width of a graph by its strong colouring numbers. In particular, we show that for every $r\in \mathbb{N}$, every graph $G$ has $\text{copwidth}_r(G)\leq \text{scol}_{4r}(G)$. This implies that every class of graphs with linear strong colouring numbers has linear cop-width and linear flip-width. We use this result to deduce improved bounds for cop-width and flip-width for various sparse graph classes.

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Robert Hickingbotham. 2023-09-11. Cop-width, flip-width and strong colouring numbers. https://doi.org/10.46298/dmtcs.14976

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