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- W2000527287 abstract "A block-colouring of a 4-cycle system (V,B) of order v=1+8k is a mapping ϕ:B→C, where C is a set of colours. Every vertex of a 4-cycle system of order v=8k+1 is contained in r=v−12=4k blocks and r is called, using the graph theoretic terminology, the degree or the repetition number. A partition of degree r into s parts defines a colouring of type s in which the blocks containing a vertex x are coloured exactly with s colours. For a vertex x and for i=1,2,…,s, let Bx,i be the set of all the blocks incident with x and coloured with the ith colour. A colouring of type s is equitable if, for every vertex x, we have |Bx,i−Bx,j|≤1, for all i,j=1,…,s. In this paper we study bicolourings, tricolourings and quadricolourings, i.e. the equitable colourings of type s with s=2, s=3 and s=4, for 4-cycle systems." @default.
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- W2000527287 date "2010-11-01" @default.
- W2000527287 modified "2023-09-27" @default.
- W2000527287 title "Equitable specialized block-colourings for 4-cycle systems—I" @default.
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- W2000527287 doi "https://doi.org/10.1016/j.disc.2009.06.032" @default.
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