The minimum degree of minimal Ramsey graphs for cliques

We prove that s r ( K k ) = O 5 / 2 $s_r(K_k) O(k^5 r^{5/2})$ , where $s_r(K_k)$ is the Ramsey parameter introduced by Burr, Erdős and Lovász in 1976, which defined as smallest minimum degree of a graph G $G$ such any $r$ -colouring edges contains monochromatic $K_k$ whereas no proper subgraph has this property. The construction used our proof relies on group theoretic model generalised quadrangles Kantor 1980.