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).
Published Version
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