$k$-chromatic graph is called $k$-critical if removal of any vertex from graph makes it $k - 1$ vertex colorable.
Now i have to prove that if $G$ is a $k$ critical graph then it cannot have $k+1$ vertices.
I can see that the property is true as a triangle is 3 critical. Also we have a 5-cycle as 3 critical but no $4$ vertex graph is $3$ critical.
Can any one help me in what direction i should prove the theorem