Journal of Combinatorial Theory Series B
Distance-hereditary graphs, Steiner trees, and connected domination
SIAM Journal on Computing
Discrete Applied Mathematics - Computational combinatiorics
Recognizing P4-sparse graphs in linear time
SIAM Journal on Computing
Graph classes: a survey
Efficient and practical modular decomposition
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Fully dynamic algorithms for chordal graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete 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
On-Line Recognition of Interval Graphs in O(m + nlog n) Time
Selected papers from the 8th Franco-Japanese and 4th Franco-Chinese Conference on Combinatorics and Computer Science
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)
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
Fully dynamic algorithm for recognition and modular decomposition of permutation graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Fully-Dynamic recognition algorithm and certificate for directed cographs
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in 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
Theoretical Computer Science
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The problem of dynamically recognizing a class of graphs has received much attention recently. Given an input graph and a sequence of operations (vertex and edge additions and deletions) to be performed on that graph, the algorithm must determine after each operation if the resulting graph is still a member of the class in question. This paper presents the first dynamic recognition algorithm for distance-hereditary graphs. The algorithm handles edge additions and deletions, and is optimal in that each operation can be performed in constant time. In doing so, the paper completely characterizes when an edge can be added to and removed from a distance-hereditary graph with the result remaining distance-hereditary, and develops a new representation for these graphs in terms of cographs.