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Pré-Publication, Document De Travail Année : 2015

On powers of interval graphs and their orders

Résumé

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.

Dates et versions

hal-01198830 , version 1 (14-09-2015)

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Florent Foucaud, Reza Naserasr, Aline Parreau, Petru Valicov. On powers of interval graphs and their orders. 2015. ⟨hal-01198830⟩
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