Discrete Applied Mathematics
Discrete Applied Mathematics - Combinatorial Optimization
Discrete Applied Mathematics
Efficient and practical algorithms for sequential modular decomposition
Journal of Algorithms
A New Linear Algorithm for Modular Decomposition
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Discrete Applied Mathematics
Characterisations and linear-time recognition of probe cographs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Partitioned probe comparability graphs
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in 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
On the recognition of probe graphs of some self-complementary classes of perfect graphs
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Recognition of probe ptolemaic graphs
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Recognition of probe distance-hereditary graphs
Discrete Applied Mathematics
Black-and-white threshold graphs
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
Black-and-white threshold graphs
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
Hi-index | 5.23 |
An undirected graph G=(V,E) is a probeC graph if its vertex set can be partitioned into two sets, N (nonprobes) and P (probes) where N is independent and there exists E^'@?NxN such that G^'=(V,E@?E^') is a C graph. In this article we investigate probe threshold and probe trivially perfect graphs and characterise them in terms of certain 2-Sat formulas and in other ways. For the case when the partition into probes and nonprobes is given, we give characterisations by forbidden induced subgraphs, linear recognition algorithms (in the case of probe threshold graphs it is based on the degree sequence of the graph), and linear algorithms to find a set E^' of minimum size. Furthermore, we give linear time recognition algorithms for both classes and a characterisation by forbidden subgraphs for probe threshold graphs when the partition (P,N) is not given.