Intersection graphs of paths in a tree
Journal of Combinatorial Theory Series B
Counting clique trees and computing perfect elimination schemes in parallel
Information Processing Letters
A fast algorithm for reordering sparse matrices for parallel factorization
SIAM Journal on Scientific and Statistical Computing
Graph classes: a survey
The ultimate interval graph recognition algorithm?
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
A Fully Dynamic Algorithm for Recognizing and Representing Proper Interval Graphs
SIAM Journal on Computing
Chordal Graphs and Their Clique Graphs
WG '95 Proceedings of the 21st International Workshop on Graph-Theoretic Concepts in Computer Science
Journal of Functional Programming
Journal of Computer and System Sciences
Laminar structure of ptolemaic graphs and its applications
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
A Fully Dynamic Graph Algorithm for Recognizing Proper Interval Graphs
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
A simple algorithm to find Hamiltonian cycles in proper interval graphs
Information Processing Letters
Resource allocation with time intervals
Theoretical Computer Science
Computing role assignments of proper interval graphs in polynomial time
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Computing role assignments of proper interval graphs in polynomial time
Journal of Discrete Algorithms
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We present a new representation of a chordal graph called the clique-separator graph, whose nodes are the maximal cliques and minimal vertex separators of the graph. We present structural properties of the clique-separator graph and additional properties when the chordal graph is an interval graph, proper interval graph, or split graph. We also characterize proper interval graphs and split graphs in terms of the clique-separator graph. We present an algorithm that constructs the clique-separator graph of a chordal graph in O(n^3) time and of an interval graph in O(n^2) time, where n is the number of vertices in the graph.