On the Maximum Diameter of $k$-Colorable Graphs

Abstract

We show that the diameter of connected $k$-colorable graphs with minimum degree $\geq \delta$ and order $n$ is at most $\left(3-\frac{1}{k-1}\right)\frac{n}{\delta}-1$, while for $k=3$, it is at most $\frac{57n}{23\delta}+O\left(1\right)$.