2020/06/25 by Kohayakawa, Yoshiharu, Mendonça, Walner, Mota, Guilherme Oliveira +1
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2006.14469
We investigate the problem of determining how many monochromatic trees are necessary to cover the vertices of an edge-coloured random graph. More precisely, we show that for p≫ n-1/6(ln n)1/6, in any 3-edge-colouring of the random graph G(n,p) we can find three monochromatic trees such that their union covers all vertices. This improves, for three colours, a result of Bucić, Korándi and Sudakov.