On cycle systems with specified weak chromatic number

Daniel Horsley, David Pike

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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 grater or equal to 2 and m grater or equal to 3 with (k,m) distinct from (2, 3) there is a weakly k-chromatic m-cycle system of order v for all suffciently large admissible v.
Original languageEnglish
Pages (from-to)1195 - 1206
Number of pages12
JournalJournal of Combinatorial Theory - Series A
Issue number8
Publication statusPublished - 2010
Externally publishedYes

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