Clustering and domination in perfect graphs
TLDR
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.About:
This article is published in Discrete Applied Mathematics.The article was published on 1984-09-01 and is currently open access. It has received 234 citations till now. The article focuses on the topics: Chordal graph & Maximal independent set.read more
Citations
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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.
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A linear recognition algorithm for cographs
TL;DR: This paper presents a linear time algorithm for recognizing cographs and constructing their cotree representation, which is possible to design very fast polynomial time algorithms for problems which are intractable for graphs in general.
Journal Article
Truncated power method for sparse eigenvalue problems
Xiao-Tong Yuan,Tong Zhang +1 more
TL;DR: In this paper, the authors proposed a truncated power method that can approximately solve the underlying nonconvex optimization problem of sparse eigenvalue problem, which is to extract dominant (largest) sparse Eigenvectors with at most k non-zero components.
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Clique Relaxations in Social Network Analysis: The Maximum k-Plex Problem
TL;DR: An algorithmic approach is developed exploiting the graph-theoretic properties of a k-plex that is effective in solving the problem to optimality on very large, sparse graphs such as the power law graphs frequently encountered in the applications of interest.
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Independent domination in graphs: A survey and recent results
Wayne Goddard,Michael A. Henning +1 more
TL;DR: A survey of selected recent results on independent domination in graphs is offered and it is shown that not every vertex in S is adjacent to a vertex in S .
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Book
Algorithmic graph theory and perfect graphs
TL;DR: This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems and remains a stepping stone from which the reader may embark on one of many fascinating research trails.
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Complement reducible graphs
TL;DR: It is shown that this family of graphs can be uniquely represented by a tree where the leaves of the tree correspond to the vertices of the graph.
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Algorithms for Minimum Coloring, Maximum Clique, Minimum Covering by Cliques, and Maximum Independent Set of a Chordal Graph
TL;DR: This paper presents ways for constructing efficient algorithms for finding a minimum coloring, a minimum covering by cliques, a maximum clique, and a maximum independent set given a chordal graph.