The (theta, wheel)-free graphs Part I: only-prism and only-pyramid graphs

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

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

Truemper configurations are four types of graphs (namely thetas, wheels, prisms and pyramids) that play an important role in the proof of several decomposition theorems for hereditary graph classes. In this paper, we prove two structure theorems: one for graphs with no thetas, wheels and prisms as induced subgraphs, and one for graphs with no thetas, wheels and pyramids as induced subgraphs. A consequence is a polynomial time recognition algorithms for these two classes. In Part II of this series we generalize these results to graphs with no thetas and wheels as induced subgraphs, and in Parts III and IV, using the obtained structure, we solve several optimization problems for these graphs. AMS classification: 05C75

Domaines: Mathématique discrète [cs.DM]

Emilie Diot, Marko Radovanović, Nicolas Trotignon, Kristina Vušković. The (theta, wheel)-free graphs Part I: only-prism and only-pyramid graphs. Journal of Combinatorial Theory, Series B, 2020, 143, pp.123-147. ⟨10.1016/j.jctb.2017.12.004⟩. ⟨hal-03060180⟩