Journal ArticleDOI
Domination in permutation graphs
Martin Farber,J. Mark Keil +1 more
Reads0
Chats0
TLDR
O ( n 3 ) algorithms to solve the weighted domination and weighted independent domination problems in permutation graphs, and an O ( n 2 ) algorithm to solving the cardinality domination problem inpermutation graphs are presented.About:
This article is published in Journal of Algorithms.The article was published on 1985-09-01. It has received 101 citations till now. The article focuses on the topics: Permutation graph & Permutation.read more
Citations
More filters
Journal ArticleDOI
The NP-completeness column: An ongoing guide
TL;DR: This is the fourteenth edition of a quarterly column that provides continuing coverage of new developments in the theory of NP-completeness, and readers who have results they would like mentioned (NP-hardness, PSPACE- hardness, polynomialtime-solvability, etc.), or open problems they wouldlike publicized, should send them to David S. Johnson.
Journal ArticleDOI
Bipartite permutation graphs
TL;DR: These characterizations lead to a linear time recognition algorithm, and to polynomial time algorithms for a number of NP-complete problems when restricted to graphs in this class of bipartite permutation graphs.
Journal ArticleDOI
Clustering and domination in perfect graphs
TL;DR: This paper investigates the complexity status of these problems on various sub-classes of perfect graphs, including comparability graphs, chordal graphs, bipartite graphs, split graphs, cographs and κ-trees, where the k-cluster problem is polynomial and the weighted and connected versions are studied.
Journal ArticleDOI
Bibliography on domination in graphs and some basic definitions of domination parameters
TL;DR: The following bibliography on Domination in Graphs has been compiled over the past six years at Clemson University, where it is expected that this bibliography will continue to grow at a steady rate.
Dissertation
New Width Parameters of Graphs
TL;DR: The notion of branch decompositions of a set function introduced by Robert-son and Seymour is used to introduce three new graph parameters, boolean-width, max-imum matching-width (MM-width) and maximum induced matching- width (MIM-width), which are compared to existing graph parameters by comparing partial orders of width parameters.
References
More filters
Journal ArticleDOI
Transitive Orientation of Graphs and Identification of Permutation Graphs
TL;DR: In this paper, the authors considered finite graphs with no edge joining a vertex to itself and with no two distinct edges joining the same pair of vertices, and the graphs considered in this paper are assumed to be finite.
Journal ArticleDOI
Clustering and domination in perfect graphs
TL;DR: This paper investigates the complexity status of these problems on various sub-classes of perfect graphs, including comparability graphs, chordal graphs, bipartite graphs, split graphs, cographs and κ-trees, where the k-cluster problem is polynomial and the weighted and connected versions are studied.
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
A linear algorithm for the domination number of a tree
Journal ArticleDOI
Dominating Sets in Chordal Graphs
TL;DR: It is shown that the problem of finding a minimum dominating set in a chordal graph is NP-complete, even when restricted to undirected path graphs, but exhibit a linear time greedy algorithm for the problem further restricted to directed path graphs.