1
vote
0answers
45 views

Local Lemma on lower bounding R(k,k)

We aim to prove that if $k \ge 3$ and $e2^{1-\binom{k}{2}}\binom{n}{k-2} \le 1$ then $R(k,k) >n$ Now I understand that we colour the edges of $K_n$ red and black with probability 1/2. For each ...
0
votes
1answer
84 views

Edge coloring graph vertices probability

How to show the following: Let $R(k,t)$ denote the Ramsey function, that is the minimal number $n$ so that if the edges of a complete graph $K_n$ on $n$ vertices are each colored red or blue, then ...
4
votes
3answers
160 views

Erdős Probabilistic method

My question is based on the Erdos probabilistic method. I am trying to read from the paper here. The proof of Theorem 1 contains the statement Since a block sequence is monochromatic with ...