Long induced paths in minor-closed graph classes and beyond - Université Clermont Auvergne Accéder directement au contenu
Article Dans Une Revue The Electronic Journal of Combinatorics Année : 2023

Long induced paths in minor-closed graph classes and beyond

Résumé

In this paper we show that every graph of pathwidth less than $k$ that has a path of order $n$ also has an induced path of order at least $\frac{1}{3} n^{1/k}$. This is an exponential improvement and a generalization of the polylogarithmic bounds obtained by Esperet, Lemoine and Maffray (2016) for interval graphs of bounded clique number. We complement this result with an upper-bound. This result is then used to prove the two following generalizations: - every graph of treewidth less than $k$ that has a path of order $n$ contains an induced path of order at least $\frac{1}{4} (\log n)^{1/k}$; - for every non-trivial graph class that is closed under topological minors there is a constant $d \in (0,1)$ such that every graph from this class that has a path of order $n$ contains an induced path of order at least $(\log n)^d$. We also describe consequences of these results beyond graph classes that are closed under topological minors.

Dates et versions

hal-03874817 , version 1 (28-11-2022)

Identifiants

Citer

Claire Hilaire, Jean-Florent Raymond. Long induced paths in minor-closed graph classes and beyond. The Electronic Journal of Combinatorics, 2023, 30 (1), pp.P1.18. ⟨10.37236/11029⟩. ⟨hal-03874817⟩
16 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More