On powers of interval graphs and their orders
Abstract
It was proved by Raychaudhuri in 1987 that if a graph power is an interval graph, then so is the next power . This result was extended to -trapezoid graphs by Flotow in 1995. We extend the statement for interval graphs by showing that any interval representation of can be extended to an interval representation of that induces the same left endpoint and right endpoint orders. The same holds for unit interval graphs. We also show that a similar fact does not hold for trapezoid graphs.
Keywords
Cite
@article{arxiv.1505.03459,
title = {On powers of interval graphs and their orders},
author = {Florent Foucaud and Reza Naserasr and Aline Parreau and Petru Valicov},
journal= {arXiv preprint arXiv:1505.03459},
year = {2015}
}
Comments
4 pages, 1 figure. It has come to our attention that Theorem 1, the main result of this note, follows from earlier results of [G. Agnarsson, P. Damaschke and M. M. Halldorsson. Powers of geometric intersection graphs and dispersion algorithms. Discrete Applied Mathematics 132(1-3):3-16, 2003]. This version is updated accordingly