Rk(m,n) is the least number such that for each coloring of k-subsets of {1,2,…,Rk(m,n)} with blue and red colors, there is a subset with m elements such that all of its k-subsets are red or there is a subset with n elements such that all of its k-subsets are blue.
a) If we give a direction randomly to all edges of a graph Kn then what is the probability that the resultant graph does not have directed triangles?
b) Prove that there exists a c such that R3(4,n)≥2cn. probabilitylogarithmsgraph theoryexpected valueprobability and stats