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math.CO2014
Spherical Thrackles
Grant Cairns, Timothy J. Koussas, Yuri Nikolayevsky
We establish Conway's thrackle conjecture in the case of spherical thrackles; that is, for drawings on the unit sphere where the edges are arcs of great circles.
math.CO2014
A sharp refinement of a result of Alon, Ben-Shimon and Krivelevich on bipartite graph vertex sequences
Grant Cairns, Stacey Mendan, Yuri Nikolayevsky
We give a sharp refinement of a result of Alon, Ben-Shimon and Krivelevich. This gives a sufficient condition for a finite sequence of positive integers to be the vertex degree lis…