Equivalence between pathbreadth and strong pathbreadth

Document Type

Article

Department or Administrative Unit

Computer Science

Publication Date

6-15-2019

Abstract

We say that a given graph G=(V,E) has pathbreadth at most ρ, denoted pb(G) ≤ ρ, if there exists a Robertson and Seymour’s path decomposition where every bag is contained in the ρ-neighbourhood of some vertex. Similarly, we say that G has strong pathbreadth at most ρ, denoted spb(G) ≤ ρ, if there exists a Robertson and Seymour’s path decomposition where every bag is the complete ρ-neighbourhood of some vertex. It is straightforward that pb(G) ≤ spb(G) for any graph G. Inspired from a close conjecture in Leitert and Dragan (2016), we prove in this note that spb(G) ≤ 4·pb(G).

Comments

This article was originally published in Discrete Applied Mathematics. The full-text article from the publisher can be found here.

Due to copyright restrictions, this article is not available for free download from ScholarWorks @ CWU.

Journal

Discrete Applied Mathematics

Rights

© 2019 Elsevier B.V. All rights reserved.

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