Large Sets of Wrapped K–K Hamilton Cycle Decompositions of Complete Bipartite 3‐Uniform Hypergraphs

Zhao, Hongtao; Rodger, C. A.

doi:10.1002/jcd.21423

Cited by 2 publications

(3 citation statements)

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“…A K‐K Hamilton cycle

H

K_{n, n}^{(3)}

is said to be wrapped (defined first in ) if it is of the form

H = {(a_{0}, {\overset{b}{true}}_{0}, a_{1}, {\overset{b}{true}}_{1}, \dots, a_{n - 1}, {\overset{b}{true}}_{n - 1})}_{3},

where

{a_{0}, a_{1}, \dots, a_{n - 1}} = {b_{0}, b_{1}, \dots, b_{n - 1}} = Z_{n}

, and where each consecutive triple of vertices in

H

is an edge. A K‐K Hamilton cycle decomposition of

K_{n, n}^{(3)}

is said to be wrapped if each K‐K Hamilton cycle in the decomposition is wrapped.…”

Section: Introductionmentioning

confidence: 99%

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Large sets of Hamilton cycle decompositions of complete bipartite 3‐uniform hypergraphs

Zhao

2018

J of Combinatorial Designs

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Using the Katona-Kierstead (K-K) definition of a Hamilton cycle in a uniform hypergraph, we investigate the existence of large sets of wrapped K-K Hamilton cycle decompositions of the complete bipartite 3-uniform hypergraph K n n , (3) , settling the existence whenever n is odd. We also prove that there exists a large set of double wrapped K-K Hamilton cycle decompositions of K n n , (3) if and only if n is even. K E Y W O R D S complete bipartite 3-uniform hypergraph, Hamilton cycle, Hamilton cycle decomposition, large set k ( ) . The complete graph K n is actually a K n (2) . J Combin Des. 2018;26:581-594. wileyonlinelibrary.com/journal/jcd

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“…A K‐K Hamilton cycle

H

K_{n, n}^{(3)}

is said to be wrapped (defined first in ) if it is of the form

H = {(a_{0}, {\overset{b}{true}}_{0}, a_{1}, {\overset{b}{true}}_{1}, \dots, a_{n - 1}, {\overset{b}{true}}_{n - 1})}_{3},

where

{a_{0}, a_{1}, \dots, a_{n - 1}} = {b_{0}, b_{1}, \dots, b_{n - 1}} = Z_{n}

, and where each consecutive triple of vertices in

H

is an edge. A K‐K Hamilton cycle decomposition of

K_{n, n}^{(3)}

is said to be wrapped if each K‐K Hamilton cycle in the decomposition is wrapped.…”

Section: Introductionmentioning

confidence: 99%

“…In , the author and Rodger settled the existence of wrapped

(K_{n, n}^{(3)}, H)

‐LGD whenever

n

is prime. In this paper, we settle the existence of wrapped

(K_{n, n}^{(3)}, H)

‐LGD for odd

n

.…”

Section: Introductionmentioning

confidence: 99%

Large sets of Hamilton cycle decompositions of complete bipartite 3‐uniform hypergraphs

Zhao

2018

J of Combinatorial Designs

Self Cite

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“…There exists a complete automorphism group G of order n (The definition and properties of Complete Automorphism Groups from Reference [8]). When ( , ) 1  kn , there exist a permutation 0…”

mentioning

confidence: 99%

Large Sets of Hamilton Cycle Decompositions of a Class of Uniform Hypergraphs

Wang

2023

J. Phys.: Conf. Ser.

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Large Sets of Wrapped K–K Hamilton Cycle Decompositions of Complete Bipartite 3‐Uniform Hypergraphs

Cited by 2 publications

References 12 publications

Large sets of Hamilton cycle decompositions of complete bipartite 3‐uniform hypergraphs

Large sets of Hamilton cycle decompositions of complete bipartite 3‐uniform hypergraphs

Large Sets of Hamilton Cycle Decompositions of a Class of Uniform Hypergraphs

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