For fixed $p$ and $q$, an edge-coloring of the complete graph $K_n$ is said to be a $(p, q)$-coloring if every $K_p$ receives at least $q$ distinct colors. The function $f(n, p, q)$ minimum number colors needed for have q)$-coloring. This was introduced about 45 years ago, but studied systematically by Erd\H{o}s Gy\'{a}rf\'{a}s in 1997, now known as Erd\H{o}s-Gy\'{a}rf\'{a}s function. In this p...
