Journal of Algorithms
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
A wide-range efficient algorithm for minimal triangulation
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A polynomial time recognition algorithm for probe interval graphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Construction of probe interval models
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
How to Use the Minimal Separators of a Graph for its Chordal Triangulation
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Discrete Applied Mathematics
2-tree probe interval graphs have a large obstruction set
Discrete Applied Mathematics - Special issue: Max-algebra
Partitioned probe comparability graphs
Theoretical Computer Science
Probe Matrix Problems: Totally Balanced Matrices
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Discrete Applied Mathematics
The Simultaneous Representation Problem for Chordal, Comparability and Permutation Graphs
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
2-Tree probe interval graphs have a large obstruction set
Discrete Applied Mathematics
Theoretical Computer Science
Recognition of probe cographs and partitioned probe distance hereditary graphs
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
The PIGs full monty – a floor show of minimal separators
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Canonical data structure for interval probe graphs
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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A graph G = (V,E) is chordal probe if its vertices can be partitioned into two sets P (probes) and N (non-probes) where N is a stable set and such that G can be extended to a chordal graph by adding edges between non-probes. The study of chordal probe graphs was originally motivated as a generalization of the interval probe graphs which occur in applications involving physical mapping of DNA. However, chordal probe graphs also have their own computational biology application as a special case of constructing phylogenies, tree structures which model genetic mutations.We give several characterizations of chordal probe graphs, first in the case of a fixed given partition of the vertices into probes and non-probes, and second in the more general case where no partition is given. In both of these cases, our results are obtained by characterizing superclasses, namely, N-triangulatable graphs and cyclebicolorable graphs, which are first introduced here. We give polynomial time recognition algorithms for each class. The complexity is O (|P||E|), given a partition of the vertices into probes and non-probes, thus also providing a interesting tractible subcase of the chordal graph sandwich problem. If no partition is given in advance, the complexity of our recognition algorithm is O(|V|2|E|).