Discrete Applied Mathematics
A practical algorithm for making filled graphs minimal
Theoretical Computer Science
Measures on monotone properties of graphs
Discrete Applied Mathematics
Treewidth and Minimum Fill-in: Grouping the Minimal Separators
SIAM Journal on Computing
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Every monotone graph property is testable
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Computing Minimal Triangulations in Time O(n\alpha \log n) = o(n2.376)
SIAM Journal on Discrete Mathematics
A Linear-Time Algorithm for Finding a Maximal Planar Subgraph
SIAM Journal on Discrete Mathematics
NP-completeness results for edge modification problems
Discrete Applied Mathematics - Special issue: Traces of the Latin American conference on combinatorics, graphs and applications: a selection of papers from LACGA 2004, Santiago, Chile
Discrete Applied Mathematics
On the interval completion of chordal graphs
Discrete Applied Mathematics
Characterizing minimal interval completions towards better understanding of profile and pathwidth
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Minimal proper interval completions
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
A linear time algorithm for finding a maximal planar subgraph based on PC-trees
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Minimal split completions of graphs
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Characterizing and Computing Minimal Cograph Completions
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Cutwidth of Split Graphs, Threshold Graphs, and Proper Interval Graphs
Graph-Theoretic Concepts in Computer Science
Characterizing and computing minimal cograph completions
Discrete Applied Mathematics
Hi-index | 0.00 |
We study graph properties that admit an increasing, or equivalently decreasing, sequence of graphs on the same vertex set such that for any two consecutive graphs in the sequence their difference is a single edge. This is useful for characterizing and computing minimal completions and deletions of arbitrary graphs into having these properties. We prove that threshold graphs and chain graphs admit such sequences. Based on this characterization and other structural properties, we present linear-time algorithms both for computing minimal completions and deletions into threshold, chain, and bipartite graphs, and for extracting a minimal completion or deletion from a given completion or deletion. Minimum completions and deletions into these classes are NP-hard to compute.