2 citations · 5 across the 3 of their papers we have counts for
5 papers
Equally spaced collinear points in Euclidean Ramsey theory
Andrii Arman, Sergei Tsaturian
It is proved that for , if the points of -dimensional Euclidean space are coloured in red and blue, then there are either two red points distance one apart or blu…
A Euclidean Ramsey result in the plane
Sergei Tsaturian
An old question in Euclidean Ramsey theory asks, if the points in the plane are red-blue coloured, does there always exist a red pair of points at unit distance or five blue points…
A result in asymmetric Euclidean Ramsey theory
Andrii Arman, Sergei Tsaturian
It is proved that if the points of the three-dimensional Euclidean space are coloured in red and blue, then there exist either two red points unit distance apart, or six collinear…
The maximum number of cycles in a graph with fixed number of edges
Andrii Arman, Sergei Tsaturian
The main topic considered is maximizing the number of cycles in a graph with given number of edges. In 2009, Király conjectured that there is constant such that any graph with…
Triangle-free graphs with the maximum number of cycles
Andrii Arman, David S. Gunderson, Sergei Tsaturian
It is shown that for , among all triangle-free graphs on vertices, the complete equibipartite graph is the unique triangle-free graph with the greatest number of cyc…