Gallai partition for edge coloring Reminder: If G is an edge-coloured complete graph on at least two vertices without a rainbow triangle, there is a nontrivial partition $P$ of $V(G)$ satisfying:
(1) If $A,B \in P$ satisfy P $A \not= B$, then all edges with one end in A and the other in B have the same colour.
(2) The set of edges with ends in distinct blocks of $P$ has at most two colours.
I have no idea why it is correct. i did not found any proof in english for this over the internet. I did how ever find the original paper but it is written in Hungarian, and i do not know this language.
can someone explain in english why this statement is correct or at least share with me a link to some source in english?