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Pré-Publication, Document De Travail Année : 2020

Avoidable paths in graphs

Résumé

We prove a recent conjecture of Beisegel et al. that for every positive integer k, every graph containing an induced P_k also contains an avoidable P_k. Avoidability generalises the notion of simpliciality best known in the context of chordal graphs. The conjecture was only established for k in {1,2} (Ohtsuki et al. 1976, and Beisegel et al. 2019, respectively). Our result also implies a result of Chv\'atal et al. 2002, which assumed cycle restrictions. We provide a constructive and elementary proof, relying on a single trick regarding the induction hypothesis. In the line of previous works, we discuss conditions for multiple avoidable paths to exist.
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Dates et versions

hal-02402905 , version 1 (17-01-2020)

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Marthe Bonamy, Oscar Defrain, Meike Hatzel, Jocelyn Thiebaut. Avoidable paths in graphs. 2020. ⟨hal-02402905⟩
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