On cycle systems with specified weak chromatic number

Authors:
Daniel Horsley;David A. Pike
Affiliations:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, Canada A1C 5S7;Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, Canada A1C 5S7
Venue:
Journal of Combinatorial Theory Series A
Year:
2010

Citing 5
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A partial m=(2k+1)-cycle system of order n can be embedded in an m-cycle system of order (2n+1)m

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A partial 2k-cycle system of order n can be embedded in a 2k-cycle system of order kn + c(k),k ≥ 3, where c(k) is a quadratic function of k

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On balanced incomplete block designs with specified weak chromatic number

Journal of Combinatorial Theory Series A

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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.