What is the chromatic number of the complement of bipartite graph on $n$ vertices?
If I have a complete bipartite graph $K_{1,n-1}$, then its complement are two disconnected complete graphs, $K_1$ and $K_{n-1}$. Then the complement cannot be colored with less than $n-1$ colors.
But what is the minimal chromatic number of the complement?
Thank for your advices.
Best Answer
A bipartite graph with $2n$ vertices will have :