Journal ArticleDOI
Characterizations of totally balanced matrices
Richard P. Anstee,Martin Farber +1 more
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TLDR
Efficient recognition algorithms for totally balanced matrices are presented and a new completion algorithm for building a maximal totally balanced matrix from an arbitraryotally balanced matrix follows from these results.About:
This article is published in Journal of Algorithms.The article was published on 1984-06-01. It has received 106 citations till now. The article focuses on the topics: Balanced matrix & Strongly chordal graph.read more
Citations
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Journal ArticleDOI
Characterizations of strongly chordal graphs
TL;DR: Several characterizations of the class of strongly chordal graphs are presented, including a forbidden induced subgraph characterization and two characterizations in terms of totally balanced matrices, which yields a polynomial recognition algorithm.
MonographDOI
Combinatorial optimization : packing and covering
TL;DR: In this article, the authors propose a method for decomposition of perfect graphs and matrices by k-sum decomposition by k -sum, which is based on the idea of odd cyclic cycles in graphs.
Journal ArticleDOI
Domination, independent domination, and duality in strongly chordal graphs☆
TL;DR: Polynomial algorithms to locate minimum weight dominating sets and independent dominating sets in strongly chordal graphs and to efficiently solve certain optimization problems for totally balanced matrices are presented.
Journal ArticleDOI
Tractability of Parameterized Completion Problems on Chordal, Strongly Chordal, and Proper Interval Graphs
TL;DR: The parameterized complexity of three NP-hard graph completion problems, motivated by molecular biology, is studied and it is shown that the parameterized version of the strongly chordal graph completion problem is FPT by giving an O(ck m log n)-time algorithm for it.
Journal ArticleDOI
Dually Chordal Graphs
TL;DR: A unified framework for characterizations of graphs with maximum neighborhood orderings in terms of neighborhood and clique hypergraphs which have the Helly property and whose line graph is chordal is given.
References
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Book
Combinatorial problems and exercises
TL;DR: In this article, the authors present a dictionary of combinatorial phrases and concepts used in graph theory, including the sieve, the sieving, and the graph sieve.
Book ChapterDOI
A Min-Max Relation for Submodular Functions on Graphs
Jack Edmonds,Rick Giles +1 more
TL;DR: In this paper, a min-max relation for submodular functions on graphs is described, and a new combinatorial minmax equality that unifies and extends results including the matroid intersection theorem and the theorem of Lucchesi and Younger on the minimum number of edges which meet every directed cut in a graph is presented.
Journal ArticleDOI
Characterizations of strongly chordal graphs
TL;DR: Several characterizations of the class of strongly chordal graphs are presented, including a forbidden induced subgraph characterization and two characterizations in terms of totally balanced matrices, which yields a polynomial recognition algorithm.
Journal ArticleDOI
Domination, independent domination, and duality in strongly chordal graphs☆
TL;DR: Polynomial algorithms to locate minimum weight dominating sets and independent dominating sets in strongly chordal graphs and to efficiently solve certain optimization problems for totally balanced matrices are presented.