A coloring problem related to the Erdős, Faber, Lovasz conjecture (Q1117945)

The famous conjecture of Erdős, Faber and Lovasz states that if the edge set of a graph G can be covered with n copies of the complete graph on vertices such that any two of those share at most one vertex, then the chromatic number of G is just n. In the paper it is shown that the chromatic number of any graph whose edge set can be covered with n copies of the complete graph on n vertices (intersection of any two of them is not restricted) is at most \(n^{3/2}\), and this bound is asymptotically best possible.