Chordal probe graphs

Authors:
Martin Charles Golumbic;Marina Lipshteyn
Affiliations:
Department of Computer Science, Caesarea Rothschild Institute, University of Haifa, Haifa, Israel;Department of Computer Science, Caesarea Rothschild Institute, University of Haifa, Haifa, Israel
Venue:
Discrete Applied Mathematics
Year:
2004

Citing 7
Cited 12

On probe interval graphs

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Graph classes: a survey

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Weakly chordal graph algorithms via handles

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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
Recognizing weakly triangulated graphs by edge separability

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Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)

Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)

Two tricks to triangulate chordal probe graphs in polynomial time

SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Probe Matrix Problems: Totally Balanced Matrices

AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
On probe permutation graphs

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
Path-Bicolorable Graphs

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Probe threshold and probe trivially perfect graphs

Theoretical Computer Science
Characterisations and linear-time recognition of probe cographs

WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Probe distance-hereditary graphs

CATS '10 Proceedings of the Sixteenth Symposium on Computing: the Australasian Theory - Volume 109
Adjacency matrices of probe interval graphs

Discrete Applied Mathematics
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
On probe permutation graphs

TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Recognition of probe distance-hereditary graphs

Discrete Applied Mathematics

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Abstract

In this paper, we introduce the class of chordal probe graphs which are a generalization of both interval probe graphs and chordal graphs. A graph G 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. We show that chordal probe graphs may contain neither an odd-length chordless cycle nor the complement of a chordless cycle, hence they are perfect graphs. We present a complete hierarchy with separating examples for chordal probe and related classes of graphs. We give polynomial time recognition algorithms for the subfamily of chordal probe graphs which are also weakly chordal, 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.