On powers of interval graphs and their orders
Résumé
It was proved by Raychaudhuri in 1987 that if a graph power Gk−1 is an interval graph, then so is the next power Gk. 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 Gk−1 can be extended to an interval representation of Gk 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.