A note on triangle-free quasi-symmetric designs

Triangle-free quasi-symmetric 2- (v, k, λ) designs with intersection numbers x, y; 0 1, are investigated. It is proved that λ⩾2y − x − 3. As a consequence it is seen that for fixed λ, there are finitely many triangle-free quasi-symmetric designs. It is also proved that: k⩽y(y − x) + x. Copyright © 2011 Wiley Periodicals, Inc. J Combin Designs 19:422-426, 2011