2017/05/12 by Arman, Andrii, Tsaturian, Sergei
#Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1705.04640
It is proved that for k≥ 4, if the points of k-dimensional Euclidean space are coloured in red and blue, then there are either two red points distance one apart or k+3 blue collinear points with distance one between any two consecutive points. This result is new for 4≤ k≤ 10.