Strong elimination ordering of the total graph of a tree
TLDR
A new linear algorithm for the minimum weight total dominating set problem for trees, given a new proof of this fact by directly constructing a strong elimination ordering.About:
This article is published in Discrete Applied Mathematics.The article was published on 1992-11-11 and is currently open access. It has received 1 citations till now. The article focuses on the topics: Chordal graph & Tree (graph theory).read more
Citations
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On the complexity of variations of mixed domination on graphs
TL;DR: This paper presents NP-completeness and MAX SNP-hardness results for some of the variations of the mixed domination problem on graphs, and presents a general framework of solving these problems and various dominating and covering problems for trees in linear time.
References
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Three partition refinement algorithms
Robert Paige,Robert E. Tarjan +1 more
TL;DR: This work presents improved partition refinement algorithms for three problems: lexicographic sorting, relational coarsest partition, and double lexical ordering that uses a new, efficient method for unmerging two sorted sets.
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Triangulated graphs and the elimination process
TL;DR: In this paper, a triangulated graph is defined as a graph in which for every cycle of length l > 3, there is an edge joining two nonconsecutive vertices.
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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.
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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.