P4-trees and substitution decomposition
Discrete Applied Mathematics
Discrete Mathematics
Discrete Mathematics
Linear-time modular decomposition and efficient transitive orientation of comparability graphs
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
An Efficient Algorithm to Recognize Prime Undirected Graphs
WG '92 Proceedings of the 18th International Workshop on Graph-Theoretic Concepts in Computer Science
Search in Indecomposable Graphs
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
A New Linear Algorithm for Modular Decomposition
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Conditionally critical indecomposable graphs
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
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A module of a graph is a non-empty subset of vertices such that every non-module vertex is either connected to all or none of the module vertices. An indecomposable graph contains no non-trivial module (modules of cardinality 1 and |V| are trivial). We present an algorithm to compute indecomposability preserving elimination sequence, which is faster by a factor of |V| compared to the algorithms based on earlier published work. The algorithm is based on a constructive proof of Ille’s theorem [9]. The proof uses the properties of X-critical graphs, a generalization of critical indecomposable graphs.