Abstract
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 (n2). 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.
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