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arXiv · 1505.03459

On powers of interval graphs and their orders

Florent Foucaud·Reza Naserasr·Aline Parreau·Petru Valicov
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Abstract

It was proved by Raychaudhuri in 1987 that if a graph power $G^{k-1}$ is an interval graph, then so is the next power $G^k$. This result was extended to $m$-trapezoid graphs by Flotow in 1995. We extend the statement for interval graphs by showing that any interval representation of $G^{k-1}$ can be extended to an interval representation of $G^k$ 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.

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Florent Foucaud, Reza Naserasr, Aline Parreau, Petru Valicov. 2015-11-09. On powers of interval graphs and their orders. https://arxiv.org/abs/1505.03459

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