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 Dec 1
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

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