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arXiv · 2408.00983

Quasi-tree-partitions of graphs with an excluded subgraph

Chun-Hung Liu·David R. Wood
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Abstract

This paper studies the structure of graphs with given tree-width and excluding a fixed complete bipartite subgraph, which generalises the bounded degree setting. We give a new structural description of such graphs in terms of so-called quasi-tree-partitions. We demonstrate the utility of this result through applications to (fractional) clustered colouring. Further generalisations of these structural and colouring results are presented.

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Chun-Hung Liu, David R. Wood. 2025-12-11. Quasi-tree-partitions of graphs with an excluded subgraph. https://arxiv.org/abs/2408.00983

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