3 years ago

# A note on simultaneous representation problem for interval and circular-arc graphs.

Jan Bok, Nikola Jedličková

In this short note, we show two NP-completeness results regarding the \emph{simultaneous representation problem}, introduced by Lubiw and Jampani.

The simultaneous representation problem for a given class of intersection graphs asks if some $k$ graphs can be represented so that every vertex is represented by the same interval in each representation. We prove that it is NP-complete to decide this for the class of interval and circular-arc graphs in the case when $k$ is a part of the input and graphs are not in a sunflower position.

Publisher URL: http://arxiv.org/abs/1811.04062

DOI: arXiv:1811.04062v1

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