Degree conditions for Hamiltonian graphs to have [a,b] -factors containing a given Hamiltonian cycle

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Let 1≤a<b be integers and G a Hamiltonian graph of order |G|≥(a+b)(2a+b)/b. Suppose that δ(G)≥a+2 and max{deg G(x),degG(y)}≥a|G|/(a+b)+2 for each pair of nonadjacent vertices x and y in G. Then G has an [a,b]-factor which is edge-disjoint from a given Hamiltonian cycle. The lower bound on the degree condition is sharp. For the case of odd a = b, there exists a graph satisfying the conditions of the theorem but having no desired factor. As consequences, we have the degree conditions for Hamiltonian graphs to have [a,b]-factors containing a given Hamiltonian cycle.

Original languageEnglish
Pages (from-to)241-250
Number of pages10
JournalDiscrete Mathematics
Volume280
Issue number1-3
DOIs
Publication statusPublished - 2004 Apr 6
Externally publishedYes

Fingerprint

Hamiltonians

Keywords

  • Connected factor
  • Degree condition
  • Factor
  • Hamiltonian graph

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Degree conditions for Hamiltonian graphs to have [a,b] -factors containing a given Hamiltonian cycle. / Matsuda, Haruhide.

In: Discrete Mathematics, Vol. 280, No. 1-3, 06.04.2004, p. 241-250.

Research output: Contribution to journalArticle

@article{9e778cbe5d66492886133e849b1d30b3,
title = "Degree conditions for Hamiltonian graphs to have [a,b] -factors containing a given Hamiltonian cycle",
abstract = "Let 1≤aG(x),degG(y)}≥a|G|/(a+b)+2 for each pair of nonadjacent vertices x and y in G. Then G has an [a,b]-factor which is edge-disjoint from a given Hamiltonian cycle. The lower bound on the degree condition is sharp. For the case of odd a = b, there exists a graph satisfying the conditions of the theorem but having no desired factor. As consequences, we have the degree conditions for Hamiltonian graphs to have [a,b]-factors containing a given Hamiltonian cycle.",
keywords = "Connected factor, Degree condition, Factor, Hamiltonian graph",
author = "Haruhide Matsuda",
year = "2004",
month = "4",
day = "6",
doi = "10.1016/j.disc.2003.10.015",
language = "English",
volume = "280",
pages = "241--250",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "1-3",

}

TY - JOUR

T1 - Degree conditions for Hamiltonian graphs to have [a,b] -factors containing a given Hamiltonian cycle

AU - Matsuda, Haruhide

PY - 2004/4/6

Y1 - 2004/4/6

N2 - Let 1≤aG(x),degG(y)}≥a|G|/(a+b)+2 for each pair of nonadjacent vertices x and y in G. Then G has an [a,b]-factor which is edge-disjoint from a given Hamiltonian cycle. The lower bound on the degree condition is sharp. For the case of odd a = b, there exists a graph satisfying the conditions of the theorem but having no desired factor. As consequences, we have the degree conditions for Hamiltonian graphs to have [a,b]-factors containing a given Hamiltonian cycle.

AB - Let 1≤aG(x),degG(y)}≥a|G|/(a+b)+2 for each pair of nonadjacent vertices x and y in G. Then G has an [a,b]-factor which is edge-disjoint from a given Hamiltonian cycle. The lower bound on the degree condition is sharp. For the case of odd a = b, there exists a graph satisfying the conditions of the theorem but having no desired factor. As consequences, we have the degree conditions for Hamiltonian graphs to have [a,b]-factors containing a given Hamiltonian cycle.

KW - Connected factor

KW - Degree condition

KW - Factor

KW - Hamiltonian graph

UR - http://www.scopus.com/inward/record.url?scp=1642406653&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1642406653&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2003.10.015

DO - 10.1016/j.disc.2003.10.015

M3 - Article

AN - SCOPUS:1642406653

VL - 280

SP - 241

EP - 250

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -