13. Crossing Numbers of Complete Graphs
Noam D. Elkies · Princeton University Press eBooks · 2017
In this thesis we prove two main results.The Triangle Conjecture asserts that the convex hull of any optimal rectilinear drawing of K n must be a triangle (for n 3).We prove that, for the larger class of pseudolinear drawings, the outer face must be a triangle.The other main result is the next step toward Guy's Conjecture that theWe show that the conjecture is true for n = 11, 12; previously the conjecture was known to be true for n 10.We also prove several minor results.iii