2 citations · 6 across the 4 of their papers we have counts for
5 papers
Increasing paths in countable graphs
Andrii Arman, Bradley Elliott, Vojtěch Rödl
In this paper we study variations of an old result by Müller, Reiterman, and the last author stating that a countable graph has a subgraph with infinite degrees if and only if in a…
Properties of the Fibonacci-sum graph
Andrii Arman, David S. Gunderson, Pak Ching Li
For each positive integer , the Fibonacci-sum graph on vertices is defined by two vertices forming an edge if and only if they sum to a Fibonacci number. It…
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 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…