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Packing cliques in 3‐uniform hypergraphs
Author(s) -
Javadi Ramin,
Poorhadi Ehsan,
Fallah Farshad
Publication year - 2020
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21717
Subject(s) - mathematics , combinatorics , constant (computer programming) , upper and lower bounds , set (abstract data type) , value (mathematics) , packing problems , discrete mathematics , statistics , computer science , mathematical analysis , programming language
For positive integers n ≥ k ≥ t , a collection B of k ‐subsets of an n ‐set X is called a t ‐packing if every t ‐subset of X appears in at most one set in B . In this paper, we investigate the existence of the maximum 3‐packings whenever n is sufficiently larger than k . When n ≢ 2( mod k − 2 ) , the optimal value for the size of a 3‐packing is settled. In other cases, lower and upper bounds are obtained where mostly differ by an additive constant depending only on k but one case that they differ by a linear bound in n .