Cop-Width, Flip-Width and Strong Colouring Numbers.
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| Title: | Cop-Width, Flip-Width and Strong Colouring Numbers. |
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| Authors: | Hickingbotham, Robert1 |
| Source: | Discrete Mathematics & Theoretical Computer Science (DMTCS). 2025, Vol. 27 Issue 2, p1-9. 9p. |
| Subjects: | Sparse graphs |
| Abstract: | Cop-width and flip-width are new families of graph parameters introduced by Toruńczyk (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 ∈ N, every graph G has copwidthr (G) ≤ scol4r(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. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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