On 2-factors with a specified number of components in line graphs

S. Chiba, Y. Egawa, J. Fujisawa, A. Saito, I. Schiermeyer, M. Tsugaki, T. Yamashita

Research output: Contribution to journalArticle

Abstract

Kaiser and Vrana [European J. Combin. 33 (2012), 924-947] showed that every 5-connected line graph of minimum degree at least 6 is hamiltonian, which gives a partial solution to Thomassen’s Conjecture on hamiltonicity of line graphs [J. Graph Theory 10 (1986), 309-324]. In this paper, we prove that every 5-connected line graph of sufficiently large order compared with a given positive integer k and of minimum degree at least 6 also has a 2-factor with exactly k cycles. In order to show this result, we investigate minimum degree conditions for the existence of such a 2-factor in hamiltonian line graphs.

Original languageEnglish
Pages (from-to)541-546
Number of pages6
JournalActa Mathematica Universitatis Comenianae
Volume88
Issue number3
Publication statusPublished - 2019 Sep 2

    Fingerprint

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Chiba, S., Egawa, Y., Fujisawa, J., Saito, A., Schiermeyer, I., Tsugaki, M., & Yamashita, T. (2019). On 2-factors with a specified number of components in line graphs. Acta Mathematica Universitatis Comenianae, 88(3), 541-546.