Discrete Mathematics - Graph colouring and variations
On the complexity of recognizing perfectly orderable graphs
Discrete Mathematics
Efficient algorithms for minimum weighted colouring of some classes of perfect graphs
Discrete Applied Mathematics
A polynomial algorithm for the parity path problem on perfectly orientable graphs
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
Linear time algorithms for graph search and connectivity determination on complement graphs
Information Processing Letters
Graph classes: a survey
Even and odd pairs in comparability and in P4-comparability graphs
Discrete Applied Mathematics
Linear-time transitive orientation
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Efficient and practical modular decomposition
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Recognition and Orientation Algorithms for P4-Comparability Graphs
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Hole and antihole detection in graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
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We consider the problem of recognizing whether a simple undirected graph is a P4-comparability graph. This problem has been considered by Ho脿ng and Reed who described an O(n4)-time algorithm for its solution, where n is the number of vertices of the given graph. Faster algorithms have recently been presented by Raschle and Simon and by Nikolopoulos and Palios; the time complexity of both algorithms is O(n + m2), where m is the number of edges of the graph.In this paper, we describe an O(nm)-time, O(n+m)-space algorithm for the recognition of P4-comparability graphs. The algorithm computes the P4s of the input graph G by means of the BFS-trees of the complement of G rooted at each of its vertices, without however explicitly computing the complement of G. Our algorithm is simple, uses simple data structures, and leads to an O(nm)-time algorithm for computing an acyclic P4- transitive orientation of a P4-comparability graph.