A neighborhood condition for graphs to have [a, b]-factors

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Let G be a graph of order n, and let a and b be integers such that 1 ≤ a < b. Then we prove that G has an [a, b]-factor if the minimum degree δ(G) ≥ a, n ≥ 2(a + b)(a + b - 1)/b and |NG(X) ∪ NG(y)| ≥ an/(a + b) for any two non-adjacent vertices x and y of G. This result is best possible in some sense and it is an extension of the result of Li and Cai (A degree condition for a graph to have [a, b]-factors, J. Graph Theory 27 (1998) 1-6).

Original languageEnglish
Pages (from-to)289-292
Number of pages4
JournalDiscrete Mathematics
Volume224
Issue number1-3
Publication statusPublished - 2000 Sep 28
Externally publishedYes

Fingerprint

Graph theory

Keywords

  • [a, b]-factor
  • Factor
  • Graph
  • Neighborhood

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

A neighborhood condition for graphs to have [a, b]-factors. / Matsuda, Haruhide.

In: Discrete Mathematics, Vol. 224, No. 1-3, 28.09.2000, p. 289-292.

Research output: Contribution to journalArticle

@article{be72708a1cd54d8781271eaa22ebd092,
title = "A neighborhood condition for graphs to have [a, b]-factors",
abstract = "Let G be a graph of order n, and let a and b be integers such that 1 ≤ a < b. Then we prove that G has an [a, b]-factor if the minimum degree δ(G) ≥ a, n ≥ 2(a + b)(a + b - 1)/b and |NG(X) ∪ NG(y)| ≥ an/(a + b) for any two non-adjacent vertices x and y of G. This result is best possible in some sense and it is an extension of the result of Li and Cai (A degree condition for a graph to have [a, b]-factors, J. Graph Theory 27 (1998) 1-6).",
keywords = "[a, b]-factor, Factor, Graph, Neighborhood",
author = "Haruhide Matsuda",
year = "2000",
month = "9",
day = "28",
language = "English",
volume = "224",
pages = "289--292",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "1-3",

}

TY - JOUR

T1 - A neighborhood condition for graphs to have [a, b]-factors

AU - Matsuda, Haruhide

PY - 2000/9/28

Y1 - 2000/9/28

N2 - Let G be a graph of order n, and let a and b be integers such that 1 ≤ a < b. Then we prove that G has an [a, b]-factor if the minimum degree δ(G) ≥ a, n ≥ 2(a + b)(a + b - 1)/b and |NG(X) ∪ NG(y)| ≥ an/(a + b) for any two non-adjacent vertices x and y of G. This result is best possible in some sense and it is an extension of the result of Li and Cai (A degree condition for a graph to have [a, b]-factors, J. Graph Theory 27 (1998) 1-6).

AB - Let G be a graph of order n, and let a and b be integers such that 1 ≤ a < b. Then we prove that G has an [a, b]-factor if the minimum degree δ(G) ≥ a, n ≥ 2(a + b)(a + b - 1)/b and |NG(X) ∪ NG(y)| ≥ an/(a + b) for any two non-adjacent vertices x and y of G. This result is best possible in some sense and it is an extension of the result of Li and Cai (A degree condition for a graph to have [a, b]-factors, J. Graph Theory 27 (1998) 1-6).

KW - [a, b]-factor

KW - Factor

KW - Graph

KW - Neighborhood

UR - http://www.scopus.com/inward/record.url?scp=0002733531&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002733531&partnerID=8YFLogxK

M3 - Article

VL - 224

SP - 289

EP - 292

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -