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Is any chordal graph an incomparability graph?

I was confused by Wikipedia’s definitions of “chordal graph“, “interval graph“, “string graph“, “comparability graph“, “incomparability graph” and the complements of these.
Wikipedia says “The complement of any interval graph is a comparability graph”. So is any chordal graph an incomparability graph?

Is there a book or survey that contains detailed description of these sorts of different perfect graphs?


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