%A Chiba, Shuya
%A Egawa, Yoshimi
%A Fujisawa, Jun
%A Saito, Akira
%A Schiermeyer, Ingo
%A Tsugaki, Masao
%A Yamashita, Tomoki
%D 2019
%T On 2-factors with a specified number of components in line graphs
%K
%X Kaiser and Vr\’{a}na [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.
%U http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1251
%J Acta Mathematica Universitatis Comenianae
%0 Journal Article
%P 541-546%V 88
%N 3
%@ 0862-9544
%8 2019-07-30