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math.CO2021
Minimum number of partial triangulations
Andrey Kupavskii, Aleksei Volostnov, Yury Yarovikov
We show that the number of partial triangulations of a set of points on the plane is at least the -nd Catalan number. This is tight for convex -gons. We also describe…
math.CO2020★ 1 cited
Wiener index and graphs, almost half of whose vertices satisfy Šoltés property
Margarita Akhmejanova, Konstantin Olmezov, Aleksei Volostnov +3
The Wiener index of a connected graph is a sum of distances between all pairs of vertices of . In 1991, Šoltés formulated the problem of finding all graphs such t…