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).
Recommended Citation
Ducoffe, G., & Leitert, A. (2019). Equivalence between pathbreadth and strong pathbreadth. Discrete Applied Mathematics, 262, 185–188. https://doi.org/10.1016/j.dam.2019.02.009
Journal
Discrete Applied Mathematics
Rights
© 2019 Elsevier B.V. All rights reserved.
Comments
This article was originally published in Discrete Applied Mathematics. The full-text article from the publisher can be found here.
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