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arXiv · 2604.01999

Tree-independence number and forbidden induced subgraphs: excluding a $6$-vertex path and a $(2,t)$-biclique

Maria Chudnovsky·Julien Codsi·J. Pascal Gollin·Martin Milanič·Varun Sivashankar
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Abstract

We show that for every positive integer ${t \geq 2}$ there exists an integer $s$ such that every graph that contains no induced subgraph isomorphic to either the $6$-vertex path or the $(2,t)$-biclique, the complete bipartite graph $K_{2,t}$, has tree-independence number at most $s$. This result makes partial progress on a conjecture of Dallard, Krnc, Kwon, Milanič, Munaro, Štorgel, and Wiederrecht.

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Maria Chudnovsky, Julien Codsi, J. Pascal Gollin, Martin Milanič, Varun Sivashankar. 2026-04-02. Tree-independence number and forbidden induced subgraphs: excluding a $6$-vertex path and a $(2,t)$-biclique. https://arxiv.org/abs/2604.01999

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