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Algorithms for outerplanar graph roots and graph roots of pathwidth at most 2.

Golovach, P.A. and Heggernes, P. and Kratsch, D. and Lima, P.T. and Paulusma, D. (2017) 'Algorithms for outerplanar graph roots and graph roots of pathwidth at most 2.', in Graph-Theoretic Concepts in Computer Science : 43rd International Workshop, WG 2017, Eindhoven, The Netherlands, June 21-23, 2017. Revised selected papers. , pp. 275-288. Lecture notes in computer science. (10520).


Deciding whether a given graph has a square root is a classical problem that has been studied extensively both from graph theoretic and from algorithmic perspectives. The problem is NP-complete in general, and consequently substantial effort has been dedicated to deciding whether a given graph has a square root that belongs to a particular graph class. There are both polynomial-time solvable and NP-complete cases, depending on the graph class. We contribute with new results in this direction. Given an arbitrary input graph G, we give polynomial-time algorithms to decide whether G has an outerplanar square root, and whether G has a square root that is of pathwidth at most 2.

Item Type:Book chapter
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Publisher statement:The final publication is available at Springer via
Date accepted:31 July 2017
Date deposited:12 July 2017
Date of first online publication:02 November 2017
Date first made open access:02 November 2018

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