Consider the complete graph on $n$ vertices, and all possible graphs that can be obtained from it by coloring its edges with exactly $n$ colors. Given one of these colored graphs, we can determine the maximum size of a complete (maximal) subgraph of it with all its edges of the same color.
I would like to get a lower bound for the size of the maximal subgraphs, as described above, over all possible colorings of the complete graph on $n$ vertices.
Any hint or result about this?