Davenport-Schnizel theory of matrices
Discrete Mathematics
Extremal Graph Theory
Topological graphs with no self-intersecting cycle of length 4
Proceedings of the nineteenth annual symposium on Computational geometry
On locally Delaunay geometric graphs
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Noncrossing Hamiltonian paths in geometric graphs
Discrete Applied Mathematics
Crossing stars in topological graphs
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
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Let G be a geometric graph with n vertices, i.e., a graph drawn in the plane with straight-line edges. It is shown that if G has no self-intersecting path of length 3, then its number of edges is O(n log n). This result is asymptotically tight. Analogous questions for curvilinear drawings and for longer paths are also considered.