Convex Geometric Graphs with No Short Self-intersecting Paths

@inproceedings{Boutin2003ConvexGG,
  title={Convex Geometric Graphs with No Short Self-intersecting Paths},
  author={Debra L. Boutin},
  year={2003}
}
Pach, Pinchasi, Tardos and Tóth proved that in a straight-line graph drawing in which no path of length 3 crosses itself (called locally planar) the number of edges can be superlinear in the number of vertices. In contrast, this paper shows that if the vertices form a convex set such a graph drawing (here named locally outerplanar) has at most a linear number of edges. As an important development toward the proof, this paper also shows that every locally outerplanar graph has a vertex of degree… CONTINUE READING