Partitioning the edge set of a hypergraph into almost regular cycles
نویسندگان
چکیده
منابع مشابه
Almost partitioning any 3-edge-coloured Kn,n into 5 monochromatic cycles
We show that for any colouring of the edges of the complete bipartite graphKn,n with 3 colours there are 5 disjoint monochromatic cycles which together cover all but o(n) of the vertices and 18 disjoint monochromatic cycles which together cover all vertices. keywords: monochromatic cycle partition, Ramsey-type problem, complete bipartite graph MSC 2010: 05C69, 05C75, 05C38.
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We prove that if H = (V (H), E(H)) is a hypergraph, γ is an edge colouring of H, and S ⊆ V (H) such that any permutation of S is an automorphism of H, then there exists a permutation π of E(H) such that |π(E)| = |E| and π(E)\S = E \S for each E ∈ E(H), and such that the edge colouring γ′ of H given by γ′(E) = γ(π−1(E)) for each E ∈ E(H) is almost regular on S. The proof is short and elementary....
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ژورنال
عنوان ژورنال: Journal of Combinatorial Designs
سال: 2018
ISSN: 1063-8539
DOI: 10.1002/jcd.21610