Thirty Essays on Geometric Graph Theory pp 541-562 | Cite as

# Construction of Locally Plane Graphs with Many Edges

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## 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.

## Notes

### Acknowledgements

The author’s research was partially supported by NSERC Grant 329527 and by OTKA Grants T-046234, AT048826, and NK-62321.

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