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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Proceedings ArticleDOI
Fuzzy Partial-Order Relations for Intervals and Interval Weighted Graphs
TL;DR: This paper establishes fuzzy partial-order relations for intervals, except only at a single point in a special case, and applies the interval partial order to extend well-known shortest path and minimum spanning tree algorithms for interval weighted graphs.
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Coloring translates and homothets of a convex body
Adrian Dumitrescu,Minghui Jiang +1 more
TL;DR: Improved upper bounds and new lower bounds are obtained on the chromatic number as a linear function of the clique number for the intersection graphs of finite families of translates and homothets of a convex body.
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On the total variation distance between the binomial random graph and the random intersection graph
TL;DR: In this article, it was shown that the variation distance between the random graph G(n,m;p) and the Erdos-Renyi graph tends to be at most 0.
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An implicit representation of chordal comparability graphs in linear time
TL;DR: A linear time algorithm is given for finding the four linear orders of chordal comparability graphs using O(n) integers so that, given two vertices, it can be determined in O(1) time whether they are adjacent, no matter how dense the graph is.
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Minimum Average Distance Clique Trees
TL;DR: This paper formalizes the compactness criterion as the average distance between nodes, and presents a characterization of clique trees that satisfies this criterion, and develops a polynomial-time algorithm to find such a clique tree.
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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.