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Parallel algorithm for cograph recognition with applications
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Journal of Parallel and Distributed Computing
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Information Processing Letters
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Discrete Applied Mathematics
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Information Processing Letters
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AWOC '88 Proceedings of the 3rd Aegean Workshop on Computing: VLSI Algorithms and Architectures
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Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
The Hamiltonian problem on distance-hereditary graphs
Discrete Applied Mathematics
An optimal parallel solution for the path cover problem on P4-sparse graphs
Journal of Parallel and Distributed Computing
NP-completeness results for some problems on subclasses of bipartite and chordal graphs
Theoretical Computer Science
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FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
The Hamiltonian problem on distance-hereditary graphs
Discrete Applied Mathematics
A polynomial solution to the k-fixed-endpoint path cover problem on proper interval graphs
Theoretical Computer Science
One sufficient condition and its applications for hamiltonian graph using its spanning subgraph
SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
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In this paper we show structural and algorithmic properties on the class of quasi-threshold graphs, or QT-graphs for short, and prove necessary and sufficient conditions for a QT-graph to be Hamiltonian. Based on these properties and conditions, we construct an efficient parallel algorithm for finding a Hamiltonian cycle in a QT-graph; for an input graph on n vertices and m edges, our algorithm takes O(log n) time and requires O(n + m) processors on the CREW PRAM model. In addition, we show that the problem of recognizing whether a QT-graph is a Hamiltonian graph and the problem of computing the Hamiltonian completion number of a nonHamiltonian QT-graph can also be solved in O(log n) time with O(n + m) processors. Our algorithms rely on O(log n)-time parallel algorithms, which we develop here, for constructing tree representations of a QT-graph; we show that a QT- graph G has a unique tree representation, that is, a tree structure which meets the structural properties of G. We also present parallel algorithms for other optimization problems on QT-graphs which run in O(log n) time using a linear number of processors.