Abstract :
Recently, the author (SIAM J. Discrete Math. 16 (2003) 99–113) has asymptotically computed (via linear programming) size Ramsey numbers involving complete bipartite graphs. Here an attempt is made to extend this method to a larger class of problems by considering the ‘simplest’ open case when one of the forbidden graphs is S1,n (the n-star K1,n with an added leaf). Although we obtain new non-trivial results such as, for example, r̂(K2,n,S1,n)=(9+o(1))n and r̂(K3,n,S1,n)=(16+o(1))n, even this ‘simple’ case remains open.
