Abstract: We present some results on the harmonious colourings of the Levi graph of a 2-design, focusing on Steiner 2-design. It is easily seen that the harmonious chromatic number of such a Levi graph is at least the number of points of the design: we study and construct Banff designs, that is designs such that this lower bound is attained.Keywords: Harmonious chromatic number, Levi graph, combinatorial designPublished in RUP: 03.11.2025; Views: 369; Downloads: 6 Full text (426,74 KB)
Abstract: Combining some difference methods with the famous Bays-Lambossy theorem and its generalizations we establish some non-trivial lower bounds on the number of cyclic 2-(v,k,1) designs up to isomorphism.Keywords: cyclic Steiner 2-design, difference family, multiplierPublished in RUP: 03.11.2025; Views: 310; Downloads: 2 Full text (449,91 KB)
