A short note on the complexity of computing strong pathbreadth

Guillaume Ducoffe 1
1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : The strong pathbreadth of a given graph G is the minimum ρ such that G admits a Robertson and Seymour's path decomposition where every bag is the complete ρ-neighbourhood of some vertex in G. We prove that deciding whether a given graph has strong pathbreadth at most one is NP-complete. The latter answers negatively to a conjecture of [Leitert and Dragan, CO-COA'16].
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Guillaume Ducoffe. A short note on the complexity of computing strong pathbreadth. Information Processing Letters, Elsevier, 2018, 133, pp.56-58. ⟨10.1016/j.ipl.2018.01.005⟩. ⟨hal-01735826⟩

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