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Trapezoid graphs and their coloring. (English) Zbl 0658.05067
The authors’ abstract: “We define trapezoid graphs, an extension of both interval and permutation graphs. We show that this new class properly contains the union of the two classes, and that trapezoid graphs are equivalent to the incomparability graphs of partially ordered sets having interval order dimension at most two. We provide an optimal coloring algorithm for trapezoid graphs that runs in time O(nk), where n is the number of nodes and k is the chromatic number of the graph. Our coloring algorithm has direct applications to channel routing on integrated circuits.”
Reviewer: R.L.Hemminger

MSC:
05C99Graph theory
05C15Coloring of graphs and hypergraphs