On tight blocking set in minimum coverings Yanxun Chang, Junling Zhou 1,2 Institute of Mathematics Beijing Jiaotong University Beijing, P. R. China Giovanni Lo Faro, Antoinette Tripodi 3,4 Department of Mathematics and Computer Science University of Messina Messina, Italy Abstract Let (X, B) be a (λK n ,G)-covering with excess E and a blocking set T . Let Γ 1 , Γ 2 , ...,Γ s be all connected components of E with at least two vertices (note that s = 0 if E = ∅). The blocking set T is called tight if further V (Γ i ) ∩ T = ∅ and V (Γ i ) ∩ (X \ T ) = ∅ for 1 ≤ i ≤ s. In this paper we give a complete solution for the existence of a minimum (λK n ,G)-covering admitting a blocking set (BS), or a tight blocking set (TBS) for any λ and when G = K 3 and G = K 3 + e. Keywords: G-design, covering,triple system, kite system, blocking set, tight blocking set (TBS) 1 Email: yxchang@bjtu.edu.cn (Y. Chang), jlzhou@bjtu.edu.cn (J. Zhou). 2 Supported by NSFC Grant 61071221. 3 Email: lofaro@unime.it (G. Lo Faro), atripodi@unime.it (A. Tripodi). 4 Supported by P.R.I.N., P.R.A. and I.N.D.A.M.(G.N.S.A.G.A.). Available online at www.sciencedirect.com Electronic Notes in Discrete Mathematics 40 (2013) 365–370 1571-0653/$ – see front matter © 2013 Elsevier B.V. All rights reserved. www.elsevier.com/locate/endm http://dx.doi.org/10.1016/j.endm.2013.05.064