A note on random greedy coloring of uniform hypergraphs

Danila D. Cherkashin; Jakub Kozik

doi:10.1002/rsa.20556

A note on random greedy coloring of uniform hypergraphs

Random Structures and Algorithms ◽

10.1002/rsa.20556 ◽

2014 ◽

Vol 47 (3) ◽

pp. 407-413 ◽

Cited By ~ 21

Author(s):

Danila D. Cherkashin ◽

Jakub Kozik

Keyword(s):

Uniform Hypergraphs ◽

Greedy Coloring

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Multipass greedy coloring of simple uniform hypergraphs

Random Structures and Algorithms ◽

10.1002/rsa.20613 ◽

2015 ◽

Vol 48 (1) ◽

pp. 125-146 ◽

Cited By ~ 5

Author(s):

Jakub Kozik

Keyword(s):

Uniform Hypergraphs ◽

Greedy Coloring

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Rainbow matchings for 3-uniform hypergraphs

Journal of Combinatorial Theory Series A ◽

10.1016/j.jcta.2021.105489 ◽

2021 ◽

Vol 183 ◽

pp. 105489

Author(s):

Hongliang Lu ◽

Xingxing Yu ◽

Xiaofan Yuan

Keyword(s):

Uniform Hypergraphs

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Hypercycle Systems of 5-Cycles in Complete 3-Uniform Hypergraphs

Mathematics ◽

10.3390/math9050484 ◽

2021 ◽

Vol 9 (5) ◽

pp. 484

Author(s):

Anita Keszler ◽

Zsolt Tuza

Keyword(s):

Element Subset ◽

Uniform Hypergraphs ◽

Vertex Set ◽

Recursive Constructions

In this paper, we consider the problem of constructing hypercycle systems of 5-cycles in complete 3-uniform hypergraphs. A hypercycle system C(r,k,v) of order v is a collection of r-uniform k-cycles on a v-element vertex set, such that each r-element subset is an edge in precisely one of those k-cycles. We present cyclic hypercycle systems C(3,5,v) of orders v=25,26,31,35,37,41,46,47,55,56, a highly symmetric construction for v=40, and cyclic 2-split constructions of orders 32,40,50,52. As a consequence, all orders v≤60 permitted by the divisibility conditions admit a C(3,5,v) system. New recursive constructions are also introduced.

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