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
Citations
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On listing, sampling, and counting the chordal graphs with edge constraints
TL;DR: The problems to list, sample, and count the chordal graphs with edge constraints are discussed, and #P-completeness results for counting problems are shown, providing a unified viewpoint from algorithms' theory to problems arising from various areas such as statistics, data mining, and numerical computation.
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NeST graphs
TL;DR: The equivalence of proper NeST graph graphs and unit NeST graphs is shown, the equivalences of fixed distance NeSTgraphs and threshold tolerance graphs are shown, and the proper containment of NeSTGraphs in weakly chordal graphs are established.
Dissertation
Approximations of Points: Combinatorics and Algorithms
TL;DR: This thesis will be on the combinatorial and algorithmic aspects of approximations of point-set data P in d-dimensional Euclidean space, and presents a polynomial-time approximation scheme for computing hitting-sets for disks in the plane.
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Networks on which hot-potato routing does not livelock
Uriel Feige,Robert Krauthgamer +1 more
TL;DR: It is shown that minimum advance algorithms never livelock on tree networks, and that maximum advance algorithms are never livelocked on triangulated networks.
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On the Approximate Compressibility of Connected Vertex Cover
TL;DR: In this article, a polynomial size approximate kernelization scheme (PSAKS) was proposed for the Connected Vertex Cover problem when parameterized by the deletion distance of the input graph to the class of cographs.
References
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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.