Bounds on the twin-width of product graphs

Pettersson, W. and Sylvester, J. (2023) Bounds on the twin-width of product graphs. Discrete Mathematics and Theoretical Computer Science, 25(1), 18. (doi: 10.46298/dmtcs.10091)

Abstract

Twin-width is a graph width parameter recently introduced by Bonnet, Kim, Thomassé & Watrigant. Given two graphs G and H and a graph product ⋆ , we address the question: is the twin-width of G⋆H bounded by a function of the twin-widths of G and H and their maximum degrees? It is known that a bound of this type holds for strong products (Bonnet, Geniet, Kim, Thomassé & Watrigant; SODA 2021). We show that bounds of the same form hold for Cartesian, tensor/direct, corona, rooted, replacement, and zig-zag products. For the lexicographical product it is known that the twin-width of the product of two graphs is exactly the maximum of the twin-widths of the individual graphs (Bonnet, Kim, Reinald, Thomassé & Watrigant; IPEC 2021). In contrast, for the modular product we show that no bound can hold. In addition, we provide examples showing many of our bounds are tight, and give improved bounds for certain classes of graphs.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Pettersson, Dr William
• Authors: Pettersson, W., and Sylvester, J.
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Discrete Mathematics and Theoretical Computer Science
• Publisher: DMTCS
• ISSN: 1462-7264
• ISSN (Online): 1365-8050
• Published Online: 09 June 2023
• Copyright Holders: Copyright © 2023 by the author(s)
• First Published: First published in Discrete Mathematics and Theoretical Computer Science 25(1):18
• Publisher Policy: Reproduced under a Creative Commons license

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
305944		Multilayer Algorithmics to Leverage Graph Structure	Kitty Meeks	Engineering and Physical Sciences Research Council (EPSRC)	EP/T004878/1	M&S - Statistics