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

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


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.


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


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Copyright information

© 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

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