Recognising the overlap graphs of subtrees of restricted trees is hard

Enright, J. and Pergel, M. (2019) Recognising the overlap graphs of subtrees of restricted trees is hard. Acta Mathematica Universitatis Comenianae, 88(3), pp. 651-658.

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Publisher's URL: http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1198

Abstract

The overlap graphs of subtrees in a tree (SOGs) generalise many other graphs classes with set representation characterisations. The complexity of recognising SOGs is open. The complexities of recognising many subclasses of SOGs are known. Weconsider several subclasses of SOGs by restricting the underlying tree. For a fixed integer $k \geq 3$, we consider:\begin{my_itemize} \item The overlap graphs of subtrees in a tree where that tree has $k$ leaves \item The overlap graphs of subtrees in trees that can be derived from a given input tree by subdivision and have at least 3 leaves \item The overlap and intersection graphs of paths in a tree where that tree has maximum degree $k$\end{my_itemize} We show that the recognition problems of these classes are NP-complete. For all other parameters we get circle graphs, well known to be polynomially recognizable.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Enright, Dr Jessica
Authors: Enright, J., and Pergel, M.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Acta Mathematica Universitatis Comenianae
Publisher:Comenius University, Faculty of Mathematics, Physics and Informatics
ISSN:0862-9544
Copyright Holders:Copyright © 2019 Acta Mathematica Universitatis Comenianae
First Published:First published in Acta Mathematica Universitatis Comenianae 88(3): 651-658
Publisher Policy:Reproduced with the permission of the Publisher

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