# Polynomial Time Recognition of Squares of Ptolemaic Graphs and 3-sun-free Split Graphs

• Van Bang Le
• Andrea Oversberg
• Oliver Schaudt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8747)

## Abstract

The square of a graph $$G$$, denoted $$G^2$$, is obtained from $$G$$ by putting an edge between two distinct vertices whenever their distance is two. Then $$G$$ is called a square root of $$G^2$$. Deciding whether a given graph has a square root is known to be NP-complete, even if the root is required to be a chordal graph or even a split graph.

We present a polynomial time algorithm that decides whether a given graph has a ptolemaic square root. If such a root exists, our algorithm computes one with a minimum number of edges.

In the second part of our paper, we give a characterization of the graphs that admit a 3-sun-free split square root. This characterization yields a polynomial time algorithm to decide whether a given graph has such a root, and if so, to compute one.

## Keywords

Square of graph Square of ptolemaic graph Square of split graph Recognition algorithm

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© Springer International Publishing Switzerland 2014

## Authors and Affiliations

• Van Bang Le
• 1
Email author
• Andrea Oversberg
• 2
• Oliver Schaudt
• 2
1. 1.Institut Für InformatikUniversität RostockRostockGermany
2. 2.Institut Für InformatikUniversität zu KölnKölnGermany