R(3,4)

# program for determining all distinct red/blue-colourings of K_8 which do not have a red K_3 or a blue K_4# you can run this code on SageMath, either by using the cloud (CoCalc) or by installing it on your machine# go to http://www.sagemath.org/L = graphs.nauty_geng(8) # generates all graphs on 8 vertices with exactly one graph from each isomorphism class# it uses the program called nauty, created by Brendan McKay, for doing so Red = [G for G in L if G.clique_number() < 3 and G.complement().clique_number() < 4] # filters out those graphs which have no clique of size 3 and no independent set of size 4print len(Red)# the number of elements in the set "Red"

# we will now plot these 3 graphsfor G in Red:     G.plot()