Journal ArticleDOI
Applications of the crossing number
TLDR
A partial answer to a dual version of a well-known problem of Avital-Hanani, Erdós, Kupitz, Perles, and others, where any piecewise linear one-to-one mappingf∶R2→R2 withf(pi)=qi (1≤i≤n) is composed of at least Ω(n2) linear pieces.Abstract:
Keywords: crossing number ; bisection width of a graph Note: Professor Pach's number: [105]. Also in: Proc. 10th ACM Symposium on Computational Geometry, 1994, 198-202. Reference DCG-ARTICLE-1996-001 Record created on 2008-11-14, modified on 2017-05-12read more
Citations
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A survey of graph layout problems
TL;DR: A complete view of the current state of the art with respect to layout problems from an algorithmic point of view is presented.
Journal ArticleDOI
Planarizing Graphs | A Survey and Annotated Bibliography
TL;DR: Given a nite, undirected, simple graph G, this work is concerned with operations on G that transform it into a planar graph and gives a survey of results about such operations and related graph parameters.
Journal ArticleDOI
Experiments on the minimum linear arrangement problem
TL;DR: This paper experimentally compares several algorithms to obtain upper and lower bounds for the Minimum Linear Arrangement problem and finds that the best approximations are usually obtained using Simulated Annealing, which involves a large amount of computation time.
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A Survey on Graph Drawing Beyond Planarity
TL;DR: The aim of this survey is to describe the main research directions, the most prominent known results, and some of the most challenging open problems inGraph Drawing Beyond Planarity.
Journal ArticleDOI
A Survey on Graph Drawing Beyond Planarity.
TL;DR: Graph drawing beyond planarity is a rapidly growing research area that classifies and studies geometric representations of non-planar graphs in terms of forbidden crossing configurations as mentioned in this paper, and the main research directions in this area, the most prominent known results, and some of the most challenging open problems.
References
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Book
The Probabilistic Method
TL;DR: A particular set of problems - all dealing with “good” colorings of an underlying set of points relative to a given family of sets - is explored.
Journal ArticleDOI
A Separator Theorem for Planar Graphs
TL;DR: In this paper, it was shown that the vertices of a planar graph can be partitioned into three sets A, B, C such that no edge joins a vertex in A with another vertex in B, neither A nor B contains more than ${2n/3}$ vertices, and C contains no more than $2.
A separator theorem for planar graphs
TL;DR: In this paper, it was shown that the vertices of a planar graph can be partitioned into three sets A,B,C such that no edge joins a vertex in A with another vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than $2.
Journal ArticleDOI
On Sets of Distances of n Points
TL;DR: In this paper, the sets of distances of n points have been studied in the setting of sets of points, and the American Mathematical Monthly: Vol. 53, No. 5, pp. 248-250.