On cycle systems with specified weak chromatic number |
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Authors: | Daniel Horsley David A Pike |
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Institution: | Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, Canada A1C 5S7 |
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Abstract: | A weak k-colouring of an m-cycle system is a colouring of the vertices of the system with k colours in such a way that no cycle of the system has all of its vertices receive the same colour. An m-cycle system is said to be weakly k-chromatic if it has a weak k-colouring but no weak (k−1)-colouring. In this paper we show that for all k?2 and m?3 with (k,m)≠(2,3) there is a weakly k-chromatic m-cycle system of order v for all sufficiently large admissible v. |
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Keywords: | Cycle systems Weak colourings Embeddings Weak chromatic numbers |
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