| Autor: |
Dujmović, Vida, Hickingbotham, Robert, Hodor, Jędrzej, Joret, Gweanël, La, Hoang, Micek, Piotr, Morin, Pat, Rambaud, Clément, Wood, David R. |
| Rok vydání: |
2023 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We prove that for every planar graph $X$ of treedepth $h$, there exists a positive integer $c$ such that for every $X$-minor-free graph $G$, there exists a graph $H$ of treewidth at most $f(h)$ such that $G$ is isomorphic to a subgraph of $H\boxtimes K_c$. This is a qualitative strengthening of the Grid-Minor Theorem of Robertson and Seymour (JCTB 1986), and treedepth is the optimal parameter in such a result. As an example application, we use this result to improve the upper bound for weak coloring numbers of graphs excluding a fixed graph as a minor. |
| Databáze: |
arXiv |
| Externí odkaz: |
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