On 2-factors in star-free graphs

Olga Fourtounelli, Jun Fujisawa, P. Katerinis

Research output: Contribution to journalArticle

Abstract

In this paper we give a sharp minimum degree condition for a 2-connected star-free graph to have a 2-factor containing specified edges. Let G be a 2-connected K 1,n-free graph with minimum degree n + d and I ⊂ E(G). If one of the followings holds, then G has a 2-factor which contains every edge in I: i) n = 3, d ≥ 1, |I| ≤ 2 and |V(G)| ≥ 8 if |I| = 2; ii) n = 4, d ≥ 1, |I| ≤ 2 and |V(G)| ≥ 11 if |I| = 2; iii) n ≥ 5, d ≥ 1 and |I| ≤ 1; iv) n ≥ 5, d ≥ [(√4n - 3 + l)/2] and |I| ≤ 2.

Original languageEnglish
Pages (from-to)203-218
Number of pages16
JournalSUT Journal of Mathematics
Volume44
Issue number2
Publication statusPublished - 2008
Externally publishedYes

Fingerprint

Minimum Degree
Star
Degree Condition
Graph in graph theory
3D

Keywords

  • 2-factor
  • Minimum degree condition
  • Star-free graphs

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Fourtounelli, O., Fujisawa, J., & Katerinis, P. (2008). On 2-factors in star-free graphs. SUT Journal of Mathematics, 44(2), 203-218.

On 2-factors in star-free graphs. / Fourtounelli, Olga; Fujisawa, Jun; Katerinis, P.

In: SUT Journal of Mathematics, Vol. 44, No. 2, 2008, p. 203-218.

Research output: Contribution to journalArticle

Fourtounelli, O, Fujisawa, J & Katerinis, P 2008, 'On 2-factors in star-free graphs', SUT Journal of Mathematics, vol. 44, no. 2, pp. 203-218.
Fourtounelli O, Fujisawa J, Katerinis P. On 2-factors in star-free graphs. SUT Journal of Mathematics. 2008;44(2):203-218.
Fourtounelli, Olga ; Fujisawa, Jun ; Katerinis, P. / On 2-factors in star-free graphs. In: SUT Journal of Mathematics. 2008 ; Vol. 44, No. 2. pp. 203-218.
@article{581d1ce373564e6494b0e7be0460849c,
title = "On 2-factors in star-free graphs",
abstract = "In this paper we give a sharp minimum degree condition for a 2-connected star-free graph to have a 2-factor containing specified edges. Let G be a 2-connected K 1,n-free graph with minimum degree n + d and I ⊂ E(G). If one of the followings holds, then G has a 2-factor which contains every edge in I: i) n = 3, d ≥ 1, |I| ≤ 2 and |V(G)| ≥ 8 if |I| = 2; ii) n = 4, d ≥ 1, |I| ≤ 2 and |V(G)| ≥ 11 if |I| = 2; iii) n ≥ 5, d ≥ 1 and |I| ≤ 1; iv) n ≥ 5, d ≥ [(√4n - 3 + l)/2] and |I| ≤ 2.",
keywords = "2-factor, Minimum degree condition, Star-free graphs",
author = "Olga Fourtounelli and Jun Fujisawa and P. Katerinis",
year = "2008",
language = "English",
volume = "44",
pages = "203--218",
journal = "SUT Journal of Mathematics",
issn = "0916-5746",
publisher = "Science University of Tokyo",
number = "2",

}

TY - JOUR

T1 - On 2-factors in star-free graphs

AU - Fourtounelli, Olga

AU - Fujisawa, Jun

AU - Katerinis, P.

PY - 2008

Y1 - 2008

N2 - In this paper we give a sharp minimum degree condition for a 2-connected star-free graph to have a 2-factor containing specified edges. Let G be a 2-connected K 1,n-free graph with minimum degree n + d and I ⊂ E(G). If one of the followings holds, then G has a 2-factor which contains every edge in I: i) n = 3, d ≥ 1, |I| ≤ 2 and |V(G)| ≥ 8 if |I| = 2; ii) n = 4, d ≥ 1, |I| ≤ 2 and |V(G)| ≥ 11 if |I| = 2; iii) n ≥ 5, d ≥ 1 and |I| ≤ 1; iv) n ≥ 5, d ≥ [(√4n - 3 + l)/2] and |I| ≤ 2.

AB - In this paper we give a sharp minimum degree condition for a 2-connected star-free graph to have a 2-factor containing specified edges. Let G be a 2-connected K 1,n-free graph with minimum degree n + d and I ⊂ E(G). If one of the followings holds, then G has a 2-factor which contains every edge in I: i) n = 3, d ≥ 1, |I| ≤ 2 and |V(G)| ≥ 8 if |I| = 2; ii) n = 4, d ≥ 1, |I| ≤ 2 and |V(G)| ≥ 11 if |I| = 2; iii) n ≥ 5, d ≥ 1 and |I| ≤ 1; iv) n ≥ 5, d ≥ [(√4n - 3 + l)/2] and |I| ≤ 2.

KW - 2-factor

KW - Minimum degree condition

KW - Star-free graphs

UR - http://www.scopus.com/inward/record.url?scp=84857705938&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857705938&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84857705938

VL - 44

SP - 203

EP - 218

JO - SUT Journal of Mathematics

JF - SUT Journal of Mathematics

SN - 0916-5746

IS - 2

ER -