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

11/09/2018

∙

by   Jan Bok, et al.

∙

0

∙

share

In this short note, we show two NP-completeness results regarding the 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.