Three partition refinement algorithms
SIAM Journal on Computing
Doubly lexical ordering of dense 0–1 matrices
Information Processing Letters
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
On the complexity of the sandwich problems for strongly chordal graphs and chordal bipartite graphs
Theoretical Computer Science
Exact Algorithms for Treewidth and Minimum Fill-In
SIAM Journal on Computing
Characterizing and Computing Minimal Cograph Completions
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
On Listing, Sampling, and Counting the Chordal Graphs with Edge Constraints
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Theoretical Computer Science
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 split completions of graphs
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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A graph class is sandwich monotone if, for every pair of its graphs G 1 = (V ,E 1 ) and G 2 = (V ,E 2 ) with E 1 *** E 2 , there is an ordering e 1 , ..., e k of the edges in E 2 *** E 1 such that G = (V , E 1 *** {e 1 , ..., e i }) belongs to the class for every i between 1 and k . In this paper we show that strongly chordal graphs and chordal bipartite graphs are sandwich monotone, answering an open question by Bakonyi and Bono from 1997. So far, very few classes have been proved to be sandwich monotone, and the most famous of these are chordal graphs. Sandwich monotonicity of a graph class implies that minimal completions of arbitrary graphs into that class can be recognized and computed in polynomial time. For minimal completions into strongly chordal or chordal bipartite graphs no polynomial-time algorithm has been known. With our results such algorithms follow for both classes. In addition, from our results it follows that all strongly chordal graphs and all chordal bipartite graphs with edge constraints can be listed efficiently.