Computing square roots of trivially perfect and threshold graphs

Authors:
Martin Milanič;Oliver Schaudt
Affiliations:
University of Primorska, UP IAM, Muzejski trg 2, SI6000 Koper, Slovenia and University of Primorska, UP FAMNIT, Glagoljaška 8, SI6000 Koper, Slovenia;University of Cologne, Department for Computer Science, Weyertal 80, 50931 Cologne, Germany
Venue:
Discrete Applied Mathematics
Year:
2013

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Abstract

A graph H is a square root of a graph G if two vertices are adjacent in G if and only if they are at distance one or two in H. Computing a square root of a given graph is NP-hard, even when the input graph is restricted to be chordal. In this paper, we show that computing a square root can be done in linear time for a well-known subclass of chordal graphs, the class of trivially perfect graphs. This result is obtained by developing a structural characterization of graphs that have a split square root. We also develop linear time algorithms for determining whether a threshold graph given either by a degree sequence or by a separating structure has a square root.