Construction of locally plane graphs with many edges

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

Abstract

A graph drawn in the plane with straight-line edges is called a geometric graph. If no path of length at most k in a geometric graph G is self-intersecting, we call G k-locally plane. The main result of this chapter is a construction of k-locally plane graphs with a superlinear number of edges. For the proof, we develop randomized thinning procedures for edge-colored bipartite (abstract) graphs that can be applied to other problems as well.

Original languageEnglish
Title of host publicationThirty Essays on Geometric Graph Theory
PublisherSpringer New York
Pages541-562
Number of pages22
ISBN (Electronic)9781461401100
ISBN (Print)1461401097, 9781461401094
DOIs
Publication statusPublished - Jul 1 2014

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ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Tardos, G. (2014). Construction of locally plane graphs with many edges. In Thirty Essays on Geometric Graph Theory (pp. 541-562). Springer New York. https://doi.org/10.1007/978-1-4614-0110-0_29