The structure of (theta, pyramid, 1-wheel, 3-wheel)-free graphs

Abstract

In this paper, we study the class of graphs C defined by excluding the following structures as induced subgraphs: theta, pyramid, 1‐wheel, and 3‐wheel. We describe the structure of graphs in C, and we give a polynomial‐time recognition algorithm for this class. We also prove that K₄‐free graphs in C are 4‐colorable. We remark that C includes the class of chordal graphs, as well as the class of line graphs of triangle‐free graphs.

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Item Type:	Article
Authors/Creators:	Boncompagni, V Radovanović, M Vušković, K
Copyright, Publisher and Additional Information:	© 2018 Wiley Periodicals, Inc. This is the peer reviewed version of the following article: Boncompagni, V, Radovanović, M and Vušković, K (2018) The structure of (theta, pyramid, 1-wheel, 3-wheel)-free graphs. Journal of Graph Theory. ISSN 0364-9024. which has been published in final form at https://doi.org/10.1002/jgt.22415. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
Keywords:	2‐amalgams; bisimplicial cutsets; clique cutsets; decomposition; recognition algorithm; structure; vertex coloring
Dates:	Published: 4 February 2019 Published (online): 25 October 2018 Accepted: 6 July 2018
Institution:	The University of Leeds
Academic Units:	The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds)
Funding Information:	Funder Grant number EPSRC EP/K016423/1 EPSRC EP/N019660/1
Depositing User:	Symplectic Publications
Date Deposited:	07 Sep 2018 12:09
Last Modified:	25 Oct 2019 00:38
Status:	Published
Publisher:	Wiley
Identification Number:	10.1002/jgt.22415
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:135401

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The structure of (theta, pyramid, 1-wheel, 3-wheel)-free graphs

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