Friday August 31st at 4.30pm

of P, pq is an edge precisely if the line segment [p,q] contains no points aside from p and q. In 2006, Kara,

Por and Wood, conjectured that for all pairs of positive integers (k,c) there is a finite number v(k,c) such that

if |P|> v(k,c) and no k points of P are collinear, then V(P) contains a clique of size c. Despite the simplicity of this statement,

essentially no non-trivial bounds on v(k,c) are known. I will discuss some recent work on the conjecture of

Kara et.al. This is joint work with Cristina Fernandes, Yoshiharu Kohayakawa, Jos Coelho de Pina, and Yoshiko Wakabayashi.