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

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

Faculty of Business and Commerce

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	541-546
Number of pages	6
Journal	Acta Mathematica Universitatis Comenianae
Volume	88
Issue number	3
Publication status	Published - 2019 Sep 2

ASJC Scopus subject areas

Mathematics(all)

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AU - Chiba, S.

AU - Egawa, Y.

AU - Fujisawa, J.

AU - Saito, A.

AU - Schiermeyer, I.

AU - Tsugaki, M.

AU - Yamashita, T.

PY - 2019/9/2

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N2 - 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.

AB - 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.

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