The treewidth and pathwidth of graph unions

Alecu, Bogdan, Lozin, Vadim, Quiroz, Daniel A, Rabinovich, Roman, Razgon, Igor and Zamaraev, Viktor ORCID: 0000-0001-5755-4141 (2022) The treewidth and pathwidth of graph unions [Report]

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Executive Summary

Given two $n$-vertex graphs $G_1$ and $G_2$ of bounded treewidth, is there an $n$-vertex graph $G$ of bounded treewidth having subgraphs isomorphic to $G_1$ and $G_2$? Our main result is a negative answer to this question, in a strong sense: we show that the answer is no even if $G_1$ is a binary tree and $G_2$ is a ternary tree. We also provide an extensive study of cases where such `gluing' is possible. In particular, we prove that if $G_1$ has treewidth $k$ and $G_2$ has pathwidth $\ell$, then there is an $n$-vertex graph of treewidth at most $k + 3 \ell + 1$ containing both $G_1$ and $G_2$ as subgraphs.

Item Type:	Report
Uncontrolled Keywords:	math.CO, math.CO, cs.DM
Divisions:	Faculty of Science & Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	23 Feb 2022 10:39
Last Modified:	22 Apr 2026 15:50
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3149491
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