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arXiv · 2610.28865

Tree-independence number VIII. 3PC-free graphs have logarithmic tree-independence number

Maria Chudnovsky·Julien Codsi·Ajaykrishnan E S·Daniel Lokshtanov·Ilya Maier
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Abstract

A three-path-configuration is a graph consisting of three pairwise internally vertex-disjoint paths, the union of every two of which is an induced cycle of length at least four. A graph is 3PC-free if no induced subgraph of it is a three-path-configuration. We show that 3PC-free graphs have logarithmic tree-independence number, which is asymptotically best possible.

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Maria Chudnovsky, Julien Codsi, Ajaykrishnan E S, Daniel Lokshtanov, Ilya Maier. 2026-10-20. Tree-independence number VIII. 3PC-free graphs have logarithmic tree-independence number. https://arxiv.org/abs/2610.28865

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