3-perfect hamiltonian decomposition of the complete graph

Midori Kobayashi; Brendan D. McKay; Nobuaki Mutoh; Gisaku Nakamura; Chie Nara

3-perfect hamiltonian decomposition of the complete graph

Midori Kobayashi, Brendan D. McKay, Nobuaki Mutoh, Gisaku Nakamura, Chie Nara

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

4 Citations (Scopus)

Abstract

Let n ≥ 5 be an odd integer and K_n the complete graph on n vertices. Let i be an integer with 2 ≤ i ≤ (n-1)/2. A hamiltonian decomposition H of K_n is called i-perfect if the set of the chords at distance i of the hamiltonian cycles in H is the edge set of K_n. We show that there exists a 3-perfect hamiltonian decomposition of K_n for all odd n ≥ 7.

Original language	English
Pages (from-to)	219-224
Number of pages	6
Journal	Australasian Journal of Combinatorics
Volume	56
Publication status	Published - 2013

Cite this

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title = "3-perfect hamiltonian decomposition of the complete graph",

abstract = "Let n ≥ 5 be an odd integer and Kn the complete graph on n vertices. Let i be an integer with 2 ≤ i ≤ (n-1)/2. A hamiltonian decomposition H of Kn is called i-perfect if the set of the chords at distance i of the hamiltonian cycles in H is the edge set of Kn. We show that there exists a 3-perfect hamiltonian decomposition of Kn for all odd n ≥ 7.",

author = "Midori Kobayashi and McKay, {Brendan D.} and Nobuaki Mutoh and Gisaku Nakamura and Chie Nara",

year = "2013",

language = "English",

volume = "56",

pages = "219--224",

journal = "Australasian Journal of Combinatorics",

issn = "1034-4942",

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T1 - 3-perfect hamiltonian decomposition of the complete graph

AU - Kobayashi, Midori

AU - McKay, Brendan D.

AU - Mutoh, Nobuaki

AU - Nakamura, Gisaku

AU - Nara, Chie

PY - 2013

Y1 - 2013

N2 - Let n ≥ 5 be an odd integer and Kn the complete graph on n vertices. Let i be an integer with 2 ≤ i ≤ (n-1)/2. A hamiltonian decomposition H of Kn is called i-perfect if the set of the chords at distance i of the hamiltonian cycles in H is the edge set of Kn. We show that there exists a 3-perfect hamiltonian decomposition of Kn for all odd n ≥ 7.

AB - Let n ≥ 5 be an odd integer and Kn the complete graph on n vertices. Let i be an integer with 2 ≤ i ≤ (n-1)/2. A hamiltonian decomposition H of Kn is called i-perfect if the set of the chords at distance i of the hamiltonian cycles in H is the edge set of Kn. We show that there exists a 3-perfect hamiltonian decomposition of Kn for all odd n ≥ 7.

UR - http://www.scopus.com/inward/record.url?scp=84878419115&partnerID=8YFLogxK

M3 - Article

SN - 1034-4942

VL - 56

SP - 219

EP - 224

JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

ER -

3-perfect hamiltonian decomposition of the complete graph

Abstract

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