Information Processing Letters
Algorithms for weakly triangulated graphs
Discrete Applied Mathematics
Linear time algorithms for graph search and connectivity determination on complement graphs
Information Processing Letters
Weakly chordal graph algorithms via handles
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Efficient and practical algorithms for sequential modular decomposition
Journal of Algorithms
Introduction to Algorithms
Recognizing weakly triangulated graphs by edge separability
Nordic Journal of Computing
On the Recognition of P4-Comparability Graphs
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Chordless paths through three vertices
Theoretical Computer Science - Parameterized and exact computation
Improved algorithms for weakly chordal graphs
ACM Transactions on Algorithms (TALG)
MVSink: Incrementally Building In-Network Aggregation Trees
EWSN '09 Proceedings of the 6th European Conference on Wireless Sensor Networks
MAP estimation, message passing, and perfect graphs
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
A faster algorithm to recognize even-hole-free graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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In this paper, we study the problems of detecting holes and antiholes in general undirected graphs and present algorithms for them, which, for a graph on n vertices and m edges, run in O(n + m2) time and require O(nm) space; we thus provide a solution to the open problem posed by Hayward, Spinrad, and Sritharan in [12] asking for an O(n4)-time algorithm for finding holes in arbitrary graphs. The key element of the algorithms is a special type of depth-first search traversal which proceeds along P4s (i.e., chordless paths on four vertices) of the input graph. We also describe a different approach which allows us to detect antiholes in graphs that do not contain chordless cycles on 5 vertices in O(n + m2) time requiring O(n + m) space. Our algorithms are simple and can be easily used in practice. Additionally, we show how our detection algorithms can be augmented so that they return a hole or an antihole whenever such a structure is detected in the input graph; the augmentation takes O(n + m) time and space.