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A graph G is said to be 1-perfectly orientable ( 1 -p.o. for short) if it admits an orientation such that the out-neighborhood of every vertex is a clique in G . The class of 1 -p.o. graphs forms a common generalization of the classes of chordal and circular arc graphs. Even though 1 -p.o. graphs can be recognized in polynomial time, no structural characterization of 1 -p.o. graphs is known...
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