Data structures and network algorithms
Data structures and network algorithms
Implicit representation of graphs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Fast and Simple Algorithms for Recognizing Chordal Comparability Graphs and Interval Graphs
SIAM Journal on Computing
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Introduction to Algorithms
An implicit representation of chordal comparabilty graphs in linear-time
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
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Ma 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).