# Any graph of large chromatic number has many edge-disjoint cycles on one subset of vertices

In [1], Erdös and Hajnal raised the following question:

# Problem

Is it true that for every $$k$$, there is an $$F(k)$$ so that if a graph $$G$$ has chromatic number at least $$F(k)$$, then it always contains $$k$$ edge-disjoint cycles on the same set of vertices?

Bibliography
1 P. Erdös, Some recent problems and results in graph theory, Discrete Math. 164 (1997) no. 1, 93–96.