Abstract
In this paper we give a necessary condition and a sufficient condition for a graph to be a pairwise compatibility graph (PCG). Let G be a graph and let \(G^c\) be the complement of G. We show that if \(G^c\) has two disjoint chordless cycles then G is not a PCG. On the other hand, if \(G^c\) has no cycle then G is a PCG. Our conditions are the first necessary condition and the first sufficient condition for pairwise compatibility graphs in general.
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