Edge-coloured complete graphs: Connectedness of some subgraphs
The main result of the paper is as follows: If the edges of the complete graph \(K_ n\) on n vertices are coloured in such a way that there is no monochromatic separating edge set, then there is a monotone sequence \(K_ m\) of complete subgraphs on m vertices for \(m=4,...,n\) so that also \(K_ m\) does not contain a monochromatic separating edge set.
scientific article; zbMATH DE number 4101218