Discrete Mathematics - Graph colouring and variations
On the complexity of recognizing perfectly orderable graphs
Discrete Mathematics
On the complexity of recognizing a class of perfectly orderable graphs
Discrete Applied Mathematics
Meyniel weakly triangulated graphs—I: co-perfect orderability
Discrete Applied Mathematics
Graph classes: a survey
Linear-time modular decomposition and efficient transitive orientation of comparability graphs
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Finding houses and holes in graphs
Theoretical Computer Science
Introduction to algorithms
Recognition of some perfectly orderable graph classes
Discrete Applied Mathematics
Certifying LexBFS Recognition Algorithms for Proper Interval Graphs and Proper Interval Bigraphs
SIAM Journal on Discrete Mathematics
Certifying Algorithms for Recognizing Interval Graphs and Permutation Graphs
SIAM Journal on Computing
An O(nm)-time certifying algorithm for recognizing HHD-free graphs
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
| Hi-index | 5.23 |
In this paper, we consider the recognition problem on a class of perfectly orderable graphs, namely, the HHD-free graphs; such graphs do not contain any induced subgraph isomorphic to a house, a hole, or a domino. We prove properties of the HHD-free graphs which enable us to present an O(nm)-time and O(n+m)-space algorithm for determining whether a graph on n vertices and m edges is HHD-free; currently, this is the fastest algorithm for this problem. We also describe how the algorithm can be augmented to provide a certificate (an induced house, hole, or domino) whenever it decides that the input graph is not HHD-free, thus answering an open question posed by Hoang and Sritharan (Theoretical Computer Science 259 (2001) 233-244). The certificate computation requires O(n+m) additional time and O(n) space.