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cs.CG2023
Two trees are better than one
Adrian Dumitrescu, János Pach, Géza Tóth
We consider partitions of a point set into two parts, and the lengths of the minimum spanning trees of the original set and of the two parts. If denotes the length of a mini…
math.CO2023
Maximum Betti numbers of Čech complexes
Herbert Edelsbrunner, János Pach
The Upper Bound Theorem for convex polytopes implies that the -th Betti number of the Čech complex of any set of points in and any radius satisfies $β_{p} = O(…