Partitioning by monochromatic trees

Abstract

Any r-edge-coloured n-vertex complete graph Kn contains at most r monochromatic trees, all of different colours, whose vertex sets partition the vertex set of Kn, provided n≥3r4r! (1 - 1/r)3(1 - r) log r. This comes close to proving, for large n, a conjecture of Erdos, Gyárfás, and Pyber, which states that r - 1 trees suffice for all n. © 1996 Academic Press, Inc.