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math.CO2022★ 1 cited
Simple vs non-simple loops on random regular graphs
Benjamin Dozier, Jenya Sapir
In this note we solve the ``birthday problem'' for loops on random regular graphs. Namely, for fixed , we prove that on a random -regular graph with vertices, as …
math.CO2006★ 3 cited
Enumerative properties of triangulations of spherical bundles over S^1
Jacob Chestnut, Jenya Sapir, Ed Swartz
We give a complete characterization of all possible pairs (v,e), where v is the number of vertices and e is the number of edges, of any simplicial triangulation of an S^k-bundle ov…