Incremental modular decomposition
Journal of the ACM (JACM)
Recognizing P4-sparse graphs in linear time
SIAM Journal on Computing
A tree representation for P4-sparse graphs
Discrete Applied Mathematics
On extendedP4-reducible and extendedP4-sparse graphs
Theoretical Computer Science
Graph classes: a survey
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Efficient and practical algorithms for sequential modular decomposition
Journal of Algorithms
Linear-Time Representation Algorithms for Proper Circular-Arc Graphs and Proper Interval Graphs
SIAM Journal on Computing
A Fully Dynamic Algorithm for Recognizing and Representing Proper Interval Graphs
SIAM Journal on Computing
A New Linear Algorithm for Modular Decomposition
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
A fully dynamic algorithm for modular decomposition and recognition of cographs
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
Fully dynamic recognition algorithm and certificate for directed cograph
Discrete Applied Mathematics
Fully dynamic algorithms for chordal graphs and split graphs
ACM Transactions on Algorithms (TALG)
Simpler Linear-Time Modular Decomposition Via Recursive Factorizing Permutations
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Dynamically maintaining split graphs
Discrete Applied Mathematics
Fully Dynamic Representations of Interval Graphs
Graph-Theoretic Concepts in Computer Science
An optimal, edges-only fully dynamic algorithm for distance-hereditary graphs
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Dynamic distance hereditary graphs using split decomposition
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
A fully dynamic algorithm for the recognition of P4-sparse graphs
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
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In this paper, we solve the dynamic recognition problem for the class of P"4-sparse graphs: the objective is to handle edge/vertex additions and deletions, to recognize if each such modification yields a P"4-sparse graph, and if yes, to update a representation of the graph. Our approach relies on maintaining the modular decomposition tree of the graph, which we use for solving the recognition problem. We establish properties for each modification to yield a P"4-sparse graph and obtain a fully dynamic recognition algorithm which handles edge modifications in O(1) time and vertex modifications in O(d) time for a vertex of degree d. Thus, our algorithm implies an optimal edges-only dynamic algorithm and a new optimal incremental algorithm for P"4-sparse graphs.