  Lehel conjectured in the 1970s that every red and blue edge-coloured complete
graph can be partitioned into two monochromatic cycles. This was confirmed in
2010 by Bessy and Thomass\'e. However, the host graph $G$ does not have to be
complete. It it suffices to require that $G$ has minimum degree at least
$3n/4$, where $n$ is the order of $G$, as was shown recently by Letzter,
confirming a conjecture of Balogh, Bar\'{a}t, Gerbner, Gy\'arf\'as and
S\'ark\"ozy. This degree condition is asymptotically tight.
  Here we continue this line of research, by proving that for every red and
blue edge-colouring of an $n$-vertex graph of minimum degree at least $2n/3 +
o(n)$, there is a partition of the vertex set into three monochromatic cycles.
This approximately verifies a conjecture of Pokrovskiy and is essentially
tight.
