Cyclic type factorizations of complete bipartite graphs into hypercubes

Dalibor Fronček

Cyclic type factorizations of complete bipartite graphs into hypercubes

Dalibor Fronček

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

So far, the smallest complete bipartite graph which was known to have a cyclic type decomposition into cubes Q_d of a given dimension d was K_d2d-2,_d2d-2. Using binary Hamming codes we prove in this paper that there exists a cyclic type factorization of K₂d-1,₂d-1 into Q_d if and only if d is a power of 2.

Original language	English (US)
Pages (from-to)	201-209
Number of pages	9
Journal	Australasian Journal of Combinatorics
Volume	25
State	Published - Dec 1 2002

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title = "Cyclic type factorizations of complete bipartite graphs into hypercubes",

abstract = "So far, the smallest complete bipartite graph which was known to have a cyclic type decomposition into cubes Qd of a given dimension d was Kd2d-2,d2d-2. Using binary Hamming codes we prove in this paper that there exists a cyclic type factorization of K2d-1,2d-1 into Qd if and only if d is a power of 2.",

author = "Dalibor Fron{\v c}ek",

year = "2002",

month = dec,

day = "1",

language = "English (US)",

volume = "25",

pages = "201--209",

journal = "Australasian Journal of Combinatorics",

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publisher = "University of Queensland Press",

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T1 - Cyclic type factorizations of complete bipartite graphs into hypercubes

AU - Fronček, Dalibor

PY - 2002/12/1

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N2 - So far, the smallest complete bipartite graph which was known to have a cyclic type decomposition into cubes Qd of a given dimension d was Kd2d-2,d2d-2. Using binary Hamming codes we prove in this paper that there exists a cyclic type factorization of K2d-1,2d-1 into Qd if and only if d is a power of 2.

AB - So far, the smallest complete bipartite graph which was known to have a cyclic type decomposition into cubes Qd of a given dimension d was Kd2d-2,d2d-2. Using binary Hamming codes we prove in this paper that there exists a cyclic type factorization of K2d-1,2d-1 into Qd if and only if d is a power of 2.

UR - https://www.scopus.com/pages/publications/78650623420

UR - https://www.scopus.com/pages/publications/78650623420#tab=citedBy

M3 - Article

AN - SCOPUS:78650623420

SN - 1034-4942

VL - 25

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EP - 209

JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

ER -

Cyclic type factorizations of complete bipartite graphs into hypercubes

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