Abstract
AbstractMa and Spinrad have shown that every transitive orientation of a chordal comparability graph is the intersection of four linear orders. That is, chordal comparability graphs are comparability graphs of posets of dimension four. Among other uses, this gives an implicit representation of a chordal comparability graph using O(n) integers so that, given two vertices, it can be determined in O(1) time whether they are adjacent, no matter how dense the graph is. We give a linear-time algorithm for finding the four linear orders, improving on their bound of O(n 2).KeywordsPartial OrderLinear OrderImplicit RepresentationInterval GraphComparability GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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