Construction of Locally Plane Graphs with Many Edges

Gábor Tardos ()
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Gábor Tardos: Simon Fraser University, Rényi Institute, Budapest, Hungary; and School of Computing Science

A chapter in Thirty Essays on Geometric Graph Theory, 2013, pp 541-562 from Springer

Abstract: 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 Gk-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.

Keywords: Planar Graphs; Thinning Procedure; Geometric Graphs; Superlinear Number; Proper Edge Coloring (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-0110-0_29

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DOI: 10.1007/978-1-4614-0110-0_29

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