An incremental linear-time algorithm for recognizing interval graphs
SIAM Journal on Computing
Graphs with no induced C4 and 2K2
Discrete Mathematics
Linear recognition of pseudo-split graphs
Discrete Applied Mathematics
Split-neighbourhood graphs and the strong perfect graph conjecture
Journal of Combinatorial Theory Series B
Fixed-parameter tractability of graph modification problems for hereditary properties
Information Processing Letters
Fully dynamic algorithms for chordal graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Incremental algorithms for minimal length paths
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
A Fully Dynamic Algorithm for Recognizing and Representing Proper Interval Graphs
SIAM Journal on Computing
A new approach to dynamic all pairs shortest paths
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
European Journal of Combinatorics
Incremental algorithms in graph theory.
Incremental algorithms in graph theory.
Split-Perfect Graphs: Characterizations and Algorithmic Use
SIAM Journal on Discrete Mathematics
Interval completion with few edges
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Obtaining a planar graph by vertex deletion
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Chordal deletion is fixed-parameter tractable
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Minimal split completions of graphs
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
A fully dynamic algorithm for the recognition of P4-sparse graphs
Theoretical Computer Science
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We present an algorithm that supports operations for modifying a split graph by adding edges or vertices and deleting edges, such that after each modification the graph is repaired to become a split graph in a minimal way. In particular, if the graph is not split after the modification, the algorithm computes a minimal, or if desired even a minimum, split completion or deletion of the modified graph. The motivation for such operations is similar to the motivation for fully dynamic algorithms for particular graph classes. In our case we allow all modifications to the graph and repair, rather than allowing only the modifications that keep the graph split. Fully dynamic algorithms of the latter kind are known for split graphs [L. Ibarra, Fully dynamic algorithms for chordal graphs and split graphs, Technical Report DCS-262-IR, University of Victoria, Canada, 2000]. Our results can be used to design linear time algorithms for some recognition and completion problems, where the input is supplied in an on-line fashion.