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Concept
Trivially perfect graph
Summary
In graph theory, a trivially perfect graph is a graph with the property that in each of its induced subgraphs the size of the maximum independent set equals the number of maximal cliques. Trivially perfect graphs were first studied by but were named by ; Golumbic writes that "the name was chosen since it is trivial to show that such a graph is perfect." Trivially perfect graphs are also known as comparability graphs of trees, arborescent comparability graphs, and quasi-threshold graphs.
Trivially perfect graphs have several other equivalent characterizations:
They are the comparability graphs of order-theoretic trees. That is, let T be a partial order such that for each t ∈ T, the set {s ∈ T : s < t} is well-ordered by the relation
Official source
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