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