English

Quasi-tree-partitions of graphs with an excluded subgraph

Combinatorics 2025-12-15 v2

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.

Keywords

Cite

@article{arxiv.2408.00983,
  title  = {Quasi-tree-partitions of graphs with an excluded subgraph},
  author = {Chun-Hung Liu and David R. Wood},
  journal= {arXiv preprint arXiv:2408.00983},
  year   = {2025}
}