2014/06/20 by Paola Bonacini, Bonacini, Paola, Lucia Marino +1
Engineering · Mathematics · #05B30 #05C15 #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #math.CO #msc:05B30 #msc:05C15
paper · pdf · doi:10.48550/arxiv.1406.5454
arxiv created 2014/06/20 · openalex publication_date 2014/06/20 · arxiv updated 2014/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Σ=(X,\mathcal B) a 4-cycle system of order v=1+8k. A c-colouring of type s is a map ϕ\colon \mathcal B→ \mathcal C, with C set of colours, such that exactly c colours are used and for every vertex x all the blocks containing x are coloured exactly with s colours. Let 4k=qs+r, with q,r≥ 0. ϕ is equitable if for every vertex x the set of the 4k blocks containing x is parted in r colour classes of cardinality q+1 and s-r colour classes of cardinality q. In this paper we study colourings for which s|k, giving a description of equitable block colourings for c∈ \s,s+1,…,\lfloor\tfrac2s2+s3\rfloor \.