Colouring Steiner systems with specified block colour patterns |
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Authors: | S. Milici A. Rosa V. Voloshin |
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Affiliation: | a Universita di Catania USA b Department of Mathematics, McMaster University, Hamilton, Ontario, Canada L8S 4K1 c Moldavian Academy of Sciences USA |
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Abstract: | We consider colourings of Steiner systems S(2,3,v) and S(2,4,v) in which blocks have prescribed colour patterns, as a refinement of the classical weak colourings. The main question studied is, given an integer k, does there exist a colouring of given type using exactly k colours? For several types of colourings, a complete answer to this question is obtained while for other types, partial results are presented. We also discuss the question of the existence of uncolourable systems. |
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Keywords: | Steiner systems Colourings Block colour pattern |
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