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.
CITATION STYLE
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
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