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arXiv · 1402.0024

Polynomial time recognition of squares of ptolemaic graphs and 3-sun-free split graphs

Van Bang Le·Andrea Oversberg·Oliver Schaudt
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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.

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Van Bang Le, Andrea Oversberg, Oliver Schaudt. 2014-01-31. Polynomial time recognition of squares of ptolemaic graphs and 3-sun-free split graphs. https://arxiv.org/abs/1402.0024

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