An implicit representation of chordal comparabilty graphs in linear-time

Authors:
Andrew R. Curtis;Clemente Izurieta;Benson Joeris;Scott Lundberg;Ross M. McConnell
Affiliations:
Department of Computer Science, Colorado State University, Fort Collins, CO;Department of Computer Science, Colorado State University, Fort Collins, CO;Department of Computer Science, Colorado State University, Fort Collins, CO;Department of Computer Science, Colorado State University, Fort Collins, CO;Department of Computer Science, Colorado State University, Fort Collins, CO
Venue:
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Year:
2006

Citing 3
Cited 1

Data structures and network algorithms

Data structures and network algorithms
Modular decomposition and transitive orientation

Discrete Mathematics - Special issue on partial ordered sets
Introduction to Algorithms

Introduction to Algorithms

An implicit representation of chordal comparability graphs in linear time

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

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(n2).