Please use this identifier to cite or link to this item: https://research.matf.bg.ac.rs/handle/123456789/220
Title: The (theta, wheel)-free graphs Part I: Only-prism and only-pyramid graphs
Authors: Diot, Emilie
Radovanović, Marko 
Trotignon, Nicolas
Vušković, Kristina
Affiliations: Algebra and Mathematical Logic 
Keywords: 2-Join;Clique cutset;Decomposition;Induced subgraph;Recognition algorithm;Structure theorem;Truemper configuration
Issue Date: 1-Jul-2020
Journal: Journal of Combinatorial Theory. Series B
Abstract: 
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.
URI: https://research.matf.bg.ac.rs/handle/123456789/220
ISSN: 00958956
DOI: 10.1016/j.jctb.2017.12.004
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