TY - JOUR

T1 - On 2-factors with a specified number of components in line graphs

AU - Chiba, S.

AU - Egawa, Y.

AU - Fujisawa, J.

AU - Saito, A.

AU - Schiermeyer, I.

AU - Tsugaki, M.

AU - Yamashita, T.

N1 - Funding Information:
Received June 5, 2019. 2010 Mathematics Subject Classification. Primary 05C70, 05C45, 05C38. The work of S. C. was supported by JSPS KAKENHI Grant Numbers 17K05347, 17K05348. The work of J. F. was supported by JSPS KAKENHI Grant Number 17K05349. The work of A. S. was supported by JSPS KAKENHI Grant Number 17K00018. The work of T. Y. was supported by JSPS KAKENHI Grant Number 16K05262.

PY - 2019/9/2

Y1 - 2019/9/2

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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M3 - Article

AN - SCOPUS:85073774743

VL - 88

SP - 541

EP - 546

JO - Acta Mathematica Universitatis Comenianae

JF - Acta Mathematica Universitatis Comenianae

SN - 0862-9544

IS - 3

ER -