Journal ArticleDOI
Algorithmic graph theory and perfect graphs
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This article is published in Order.The article was published on 1986-06-01. It has received 1324 citations till now. The article focuses on the topics: Trivially perfect graph & Perfect graph theorem.read more
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Book ChapterDOI
On compact and efficient routing in certain graph classes
Feodor F. Dragan,Irina Lomonosov +1 more
TL;DR: The notion of tree-decomposition is refined by introducing acyclic (R,D)-clustering, where clusters are subsets of vertices of a graph and R and D are the maximum radius and the maximum diameter of these subsets.
Journal ArticleDOI
On the Polarity and Monopolarity of Graphs
Ross Churchley,Jing Huang +1 more
TL;DR: It is proved that recognizing polarity or monopolarity remains NP-complete for triangle-free graphs and it is shown that for claw- free graphs the former is NP- complete and the latter is polynomial time solvable.
Proceedings Article
Propagation of 2-monotone lower probabilities on an undirected graph
TL;DR: This paper presents a graphical decomposition and exact propagation algorithm for computing marginal posteriors of 2-monotone lower probabilities (equivalently, 2-alternating upper probabilities).
Proceedings ArticleDOI
Dotted interval graphs and high throughput genotyping
TL;DR: It is shown that any graph is a DIG but that DIGs in which the arithmetic progressions have a jump of at most d, form a strict hierarchy, and that coloring DIG graphs is NP-complete even for any fixed d, as well as providing a 7/8 approximation for the coloring.
Journal ArticleDOI
A k-structure generalization of the theory of 2-structures
TL;DR: The modular decomposition of k-structures is defined, and the essential algebraic properties are generalized, and it is shown that any indecomposable k-structure on n?3 nodes contains a smaller indecomPOSable substructure that has at least n-k nodes.
References
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Journal ArticleDOI
Interval graphs and related topics
TL;DR: A more general paradigm for studying various classes of graphs is suggested which can be described as follows: when 9 is allowed to be an arbitrary family of sets, the class obtained as intersection graphs is all undirected graphs.