Regular factors containing a given hamiltonian cycle

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Let k ≥ 1 be an integer and let G be a graph having a sufficiently large order n. Suppose that kn is even, the minimum degree of G is at least k + 2, and the degree sum of each pair of nonadjacent vertices in G is at least n+α, where α = 3 for odd k and α = 4 for even k. Then G has a k-factor (i.e. a k-regular spanning subgraph) which is edge-disjoint from a given Hamiltonian cycle. The lower bound on the degree condition is sharp. As a consequence, we have an Ore-type condition for graphs to have a k-factor containing a given Hamiltonian cycle.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science
EditorsJ. Akiyama, E.T. Baskoro, M. Kano
Pages123-132
Number of pages10
Volume3330
Publication statusPublished - 2005
Externally publishedYes
EventIndonesia-Japan Joint Conference on Combinatorial Geometry and Graph Theory, IJCCGGT 2003 - Bandung, Indonesia
Duration: 2003 Sep 132003 Sep 16

Other

OtherIndonesia-Japan Joint Conference on Combinatorial Geometry and Graph Theory, IJCCGGT 2003
CountryIndonesia
CityBandung
Period03/9/1303/9/16

Fingerprint

Hamiltonians
Ores

ASJC Scopus subject areas

  • Computer Science (miscellaneous)

Cite this

Matsuda, H. (2005). Regular factors containing a given hamiltonian cycle. In J. Akiyama, E. T. Baskoro, & M. Kano (Eds.), Lecture Notes in Computer Science (Vol. 3330, pp. 123-132)

Regular factors containing a given hamiltonian cycle. / Matsuda, Haruhide.

Lecture Notes in Computer Science. ed. / J. Akiyama; E.T. Baskoro; M. Kano. Vol. 3330 2005. p. 123-132.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Matsuda, H 2005, Regular factors containing a given hamiltonian cycle. in J Akiyama, ET Baskoro & M Kano (eds), Lecture Notes in Computer Science. vol. 3330, pp. 123-132, Indonesia-Japan Joint Conference on Combinatorial Geometry and Graph Theory, IJCCGGT 2003, Bandung, Indonesia, 03/9/13.
Matsuda H. Regular factors containing a given hamiltonian cycle. In Akiyama J, Baskoro ET, Kano M, editors, Lecture Notes in Computer Science. Vol. 3330. 2005. p. 123-132
Matsuda, Haruhide. / Regular factors containing a given hamiltonian cycle. Lecture Notes in Computer Science. editor / J. Akiyama ; E.T. Baskoro ; M. Kano. Vol. 3330 2005. pp. 123-132
@inproceedings{2dd18badcebf4913b74cbc6d5b16ed1a,
title = "Regular factors containing a given hamiltonian cycle",
abstract = "Let k ≥ 1 be an integer and let G be a graph having a sufficiently large order n. Suppose that kn is even, the minimum degree of G is at least k + 2, and the degree sum of each pair of nonadjacent vertices in G is at least n+α, where α = 3 for odd k and α = 4 for even k. Then G has a k-factor (i.e. a k-regular spanning subgraph) which is edge-disjoint from a given Hamiltonian cycle. The lower bound on the degree condition is sharp. As a consequence, we have an Ore-type condition for graphs to have a k-factor containing a given Hamiltonian cycle.",
author = "Haruhide Matsuda",
year = "2005",
language = "English",
volume = "3330",
pages = "123--132",
editor = "J. Akiyama and E.T. Baskoro and M. Kano",
booktitle = "Lecture Notes in Computer Science",

}

TY - GEN

T1 - Regular factors containing a given hamiltonian cycle

AU - Matsuda, Haruhide

PY - 2005

Y1 - 2005

N2 - Let k ≥ 1 be an integer and let G be a graph having a sufficiently large order n. Suppose that kn is even, the minimum degree of G is at least k + 2, and the degree sum of each pair of nonadjacent vertices in G is at least n+α, where α = 3 for odd k and α = 4 for even k. Then G has a k-factor (i.e. a k-regular spanning subgraph) which is edge-disjoint from a given Hamiltonian cycle. The lower bound on the degree condition is sharp. As a consequence, we have an Ore-type condition for graphs to have a k-factor containing a given Hamiltonian cycle.

AB - Let k ≥ 1 be an integer and let G be a graph having a sufficiently large order n. Suppose that kn is even, the minimum degree of G is at least k + 2, and the degree sum of each pair of nonadjacent vertices in G is at least n+α, where α = 3 for odd k and α = 4 for even k. Then G has a k-factor (i.e. a k-regular spanning subgraph) which is edge-disjoint from a given Hamiltonian cycle. The lower bound on the degree condition is sharp. As a consequence, we have an Ore-type condition for graphs to have a k-factor containing a given Hamiltonian cycle.

UR - http://www.scopus.com/inward/record.url?scp=23944486377&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23944486377&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:23944486377

VL - 3330

SP - 123

EP - 132

BT - Lecture Notes in Computer Science

A2 - Akiyama, J.

A2 - Baskoro, E.T.

A2 - Kano, M.

ER -