2022/09/11 by R. A. Bailey, Bailey, Robert F., Iren Darijani +1
Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2209.04946
openalex publication_date 2022/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An e-star system of order n is a decomposition of the complete graph Kn into copies of the complete bipartite graph K1,e (or e-star). Such systems are known to exist if and only if n≥ 2e and e divides \binomn2. We consider block colourings of such systems, where each e-star is assigned a colour, and two e-stars which share a vertex receive different colours. We present a computer analysis of block colourings of small 3-star systems. Furthermore, we prove that: (i) for n≡ 0,1 mod 2e there exists either an n or (n-1)-block colourable e-star system of order n; and (ii) when e=3, the same result holds in the remaining congruence classes mod 6.