The (theta, wheel)-free graphs Part IV: Induced paths and cycles

Marko Radovanović , Nicolas Trotignon (1, 2) , Kristina Vušković

1 MC2 - Modèles de calcul, Complexité, Combinatoire
2 LIP - Laboratoire de l'Informatique du Parallélisme

A hole in a graph is a chordless cycle of length at least 4. A theta is a graph formed by three internally vertex-disjoint paths of length at least 2 between the same pair of distinct vertices. A wheel is a graph formed by a hole and a node that has at least 3 neighbors in the hole. In this series of papers we study the class of graphs that do not contain as an induced subgraph a theta nor a wheel. In Part II of the series we prove a decomposition theorem for this class, that uses clique cutsets and 2-joins. In this paper we use this decomposition theorem to solve several problems related to finding induced paths and cycles in our class.

Domaines: Mathématique discrète [cs.DM]

Marko Radovanović, Nicolas Trotignon, Kristina Vušković. The (theta, wheel)-free graphs Part IV: Induced paths and cycles. Journal of Combinatorial Theory, Series B, 2021, 146, pp.495-531. ⟨10.1016/j.jctb.2020.06.002⟩. ⟨hal-03060185⟩