Maximum packings of the λ-fold complete 3-uniform hypergraph with loose 3-cycles | Zendy

Ryan C. Bunge | Zendy; Dontez Collins | Zendy; Daryl Conko-Camel | Zendy; Saad I. ElZanati | Zendy; Rachel Liebrecht | Zendy; Alexander Vasquez | Zendy

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Maximum packings of the λ-fold complete 3-uniform hypergraph with loose 3-cycles

Author(s) -

Ryan C. Bunge,

Dontez Collins,

Daryl Conko-Camel,

Saad I. ElZanati,

Rachel Liebrecht,

Alexander Vasquez

Publication year - 2020

Publication title -

opuscula mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 16

eISSN - 2300-6919

pISSN - 1232-9274

DOI - 10.7494/opmath.2020.40.2.209

Subject(s) - hypergraph , mathematics , combinatorics , lambda , fold (higher order function) , order (exchange) , physics , computer science , finance , optics , economics , programming language

It is known that the 3-uniform loose 3-cycle decomposes the complete 3-uniform hypergraph of order v if and only if v ≡ 0, 1, or 2 (mod 9). For all positive integers λ and v, we find a maximum packing with loose 3-cycles of the λ-fold complete 3-uniform hypergraph of order v. We show that, if v ≥ 6, such a packing has a leave of two or fewer edges.

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