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The "graph classes: a survey" mentioned Trotter and other authors have presented a list of forbidden subgraph of comparability graph. But the google book( where I read graph classes: a survey) do not have the page which contains the reference of specific literature. To my knowledge, one forbidden graph is "a k-cycle ( k is an odd intege $\ge$ 5) and no triangle chord". Thank you for your help in advance. :-) |
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You could refer to the entry for comparability graphs on graphclasses.org: http://www.graphclasses.org/classes/gc_72.html (look at "equivalent classes" and note that the list is not finite) |
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You must be referring to page 91 of that book. The reference is T. GALLAI, Transitiv orientierbare Graphen, Acta Math. Acad. Sci. Hung., 18 (1967), 25-66. A translation exists, but I was unable to find it online. The list is apparently also available in W.T. TROTTER, JR., Combinatorics and Partially Ordered Sets — Dimension Theory, Johns Hopkins University Press, Baltimore, London (1992). |
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