A short note on the complexity of computing strong pathbreadth

Guillaume Ducoffe (1)

1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications

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].

Mots clés: strong pathbreadth; path decomposition; acyclic clustering; graph theory; NP-complete

Domaines: Complexité [cs.CC]

Guillaume Ducoffe. A short note on the complexity of computing strong pathbreadth. Information Processing Letters, 2018, 133, pp.56-58. ⟨10.1016/j.ipl.2018.01.005⟩. ⟨hal-01735826⟩