THE TREEWIDTH AND PATHWIDTH OF GRAPH UNIONS

Bogdan Alecu; Vadim V. Lozin; Daniel A. Quiroz; Roman Rabinovich; Igor Razgon; Viktor Zamaraev

doi:10.1137/22M1524047

THE TREEWIDTH AND PATHWIDTH OF GRAPH UNIONS

Bogdan Alecu, Vadim V. Lozin, Daniel A. Quiroz, Roman Rabinovich, Igor Razgon, Viktor Zamaraev

Research output: Contribution to journal › Article › peer-review

Abstract

Given two n-vertex graphs G1 and G2 of bounded treewidth, is there an n-vertex graph G of bounded treewidth having subgraphs isomorphic to G1 and G2? Our main result is a negative answer to this question, in a strong sense: we show that the answer is no even if G1 is a binary tree and G2 is a ternary tree. We also provide an extensive study of cases where such ``gluing"" is possible. In particular, we prove that if G1 has treewidth k and G2 has pathwidth l, then there is an n-vertex graph of treewidth at most k + 3l + 1 containing both G1 and G2 as subgraphs.

Original language	English
Pages (from-to)	261-276
Number of pages	16
Journal	SIAM Journal on Discrete Mathematics
Volume	38
Issue number	1
DOIs	https://doi.org/10.1137/22M1524047
State	Published - 1 Jan 2024
Externally published	Yes

Keywords

gluing of graphs
graph union
pathwidth
treewidth

ASJC Scopus subject areas

General Mathematics

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10.1137/22M1524047

Cite this

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AU - Zamaraev, Viktor

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AB - Given two n-vertex graphs G1 and G2 of bounded treewidth, is there an n-vertex graph G of bounded treewidth having subgraphs isomorphic to G1 and G2? Our main result is a negative answer to this question, in a strong sense: we show that the answer is no even if G1 is a binary tree and G2 is a ternary tree. We also provide an extensive study of cases where such ``gluing"" is possible. In particular, we prove that if G1 has treewidth k and G2 has pathwidth l, then there is an n-vertex graph of treewidth at most k + 3l + 1 containing both G1 and G2 as subgraphs.

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THE TREEWIDTH AND PATHWIDTH OF GRAPH UNIONS

Abstract

Keywords

ASJC Scopus subject areas

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