论文信息 - 2-Colourings in S(t, t + 1, v)

2-Colourings in S(t, t + 1, v)

Let S(t, k, v) be any nontrivial Steiner system. In this paper we prove the nonexistence of 2-colourings in Steiner systems S(t, t + 1, v) when t + 1 is an odd number. Further, we prove that if t + 1 is an even number and C is a blocking set of the system S(t, t + 1, v) then ¦C¦=v/2.

Giovanni Lo Faro | Mario Gionfriddo

[1] Alexander Rosa,et al. Steiner quadruple systems - a survey , 1978, Discret. Math..

[2] Frank Harary,et al. Graph Theory , 2016 .

[3] Marialuisa J. de Resmini. On blocking sets in symmetric BIBD's with λ⩾2 , 1982 .

[4] G. Tallini. On Blocking Sets in Finite Projective and Affine Spaces , 1988 .

[6] Kevin T. Phelps,et al. Blocking sets in designs with block size four II , 1991, Discret. Math..

[7] David A. Drake. Blocking Sets in Block Designs , 1985, J. Comb. Theory, Ser. A.

[8] Kevin T. Phelps,et al. 2-Chromatic Steiner Quadruple Systems , 1980, Eur. J. Comb..

[9] Haim Hanani,et al. On Quadruple Systems , 1960, Canadian Journal of Mathematics.

[10] A. A. Bruen,et al. Blocking Sets in Affine Planes , 1983 .

[11] Kevin T. Phelps,et al. Blocking Sets in Designs with Block Size 4 , 1990, Eur. J. Comb..

[13] Chuan Yi Tang,et al. A 2.|E|-Bit Distributed Algorithm for the Directed Euler Trail Problem , 1993, Inf. Process. Lett..

[14] Hans Ludwig de Vries,et al. On property B and on Steiner systems , 1977 .