The Ramsey multiplicity of K_4

With the help of computer algorithms, we improve the lower bound on the Ramsey multiplicity of K4, and thus show that the exact value of it is equal to 9

Analysis of Exoo's Lower Bound for Ramsey number R(5,5)R(5,5)

We provide proofs to check and exposit Exoo's construction of a colouring on $K_{42}$ that demonstrates that $R(5,5)>42$. The proof suggests is also possible to extract from this construction a colouring of $K_{43}$ that has very few monochromatic $K_5$s.Comment: 15 pages, 1 figure, 3 reference