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 Absolute value of C = v/2.
机构:
Lomonosov Moscow State Univ, Moscow, RussiaLomonosov Moscow State Univ, Moscow, Russia
Demidovich, Yu. A.
Raigorodskii, A. M.
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Lomonosov Moscow State Univ, Moscow, Russia
State Univ, Moscow Inst Phys & Technol, Dolgoprudnyi, Moscow Oblast, Russia
Buryat State Univ, Ulan Ude, RussiaLomonosov Moscow State Univ, Moscow, Russia
机构:
Institute of Mathematics and Mechanics, UB RAS, Yekaterinburg 620990, S. Kovalevskoy str.
Ural Federal University, Yekaterinburg 620990Institute of Mathematics and Mechanics, UB RAS, Yekaterinburg 620990, S. Kovalevskoy str.
Gavrilyuk, Alexander L.
Goryainov, Sergey V.
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Chelyabinsk State University, Chelyabinsk 454000Institute of Mathematics and Mechanics, UB RAS, Yekaterinburg 620990, S. Kovalevskoy str.