Can anyone check if i'm correct with this question?
write down a graph H with chromatic number r but for all sufficiently large n.
So i need to find a graph with chromatic number r and contains with an extra edge. So can't i just add a vertex and join it to 2 other vertices and we get a graph with chromatic number r (just place the added vertex in a class with another vertex it is not connected to) which does contain .