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in any coloring, but has no triangle, so it is not perfect. By the perfect graph theorem, the complement of (an "odd antihole") must therefore also not be perfect. If is a cycle of five vertices, it is isomorphic to its complement, but this property is not true for longer odd cycles, and it is not as trivial to compute the clique number and chromatic number in an odd antihole as it is in an odd hole. As the strong perfect graph theorem states,

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