On almost-regular edge colourings of hypergraphs

Bryant, Darryn (2016) On almost-regular edge colourings of hypergraphs. Electronic Journal of Combinatorics, 23 4: .

Author Bryant, Darryn
Title On almost-regular edge colourings of hypergraphs
Journal name Electronic Journal of Combinatorics   Check publisher's open access policy
ISSN 1077-8926
1097-1440
Publication date 2016-10-14
Sub-type Article (original research)
Open Access Status Not yet assessed
Volume 23
Issue 4
Total pages 7
Place of publication Clemson, SC, United States
Publisher Electronic Journal of Combinatorics
Language eng
Formatted abstract
We prove that if H = (V(H), ε(H)) is a hypergraph, γ is an edge colouring of H, and SV(H) such that any permutation of S is an automorphism of H, then there exists a permutation π of ε(H) such that |π(E)| = |E| and π(E) \S = ES for each E ϵ H(H), and such that the edge colouring γ′ of H given by γ′(E) = γ(π-1(E)) for each E ϵ ε(H) is almost regular on S. The proof is short and elementary. We show that a number of known results, such as Baranyai’s Theorem on almost-regular edge colourings of complete k-uniform hypergraphs, are easy corollaries of this theorem.
Keyword Graph theory
Hypergraphs
Edge colouring
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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