Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28865

Authors: Chudnovsky, Maria, Codsi, Julien, S, Ajaykrishnan E, Lokshtanov, Daniel, Maier, Ilya

Institutions: Princeton University, University of California, Santa Barbara

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Princeton University, Air Force Office of Scientific Research

Awards: Collaborative Research: AF:Medium: Structure and Quasi-Polynomial Time Algorithms, Forbidding Induced Subgraphs: Decompositions, Coloring and Algorithms, Collaborative Research: AF:Medium: Structure and Quasi-Polynomial Time Algorithms, G7886378241

OpenAlex ID: W7223249286

Cites: 1

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Related to: 10