# Why is the Petersen graph not a perfect graph?

As I understand, a perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph. Should I show, that chromatic numbers of all Petersen's subgraphs are not equal to it clique number? Maybe there is an easier and quickly way to show that.

The Petersen graph is a Kneser graph, precisely $\text{KG}(5,2)$. By Lovasz theorem the chromatic number of $\text{KG}(n,k)$ is $n-2k+2$, hence in our case $\chi(G)=3$. On the other hand $5<6$, hence the Petersen graph is triangle-free.