Geodesic
On 2-factors with a specified number of components in line graphs
Shuya Chiba1 ; Yoshimi Egawa2 ; Jun Fujisawa3 ; Akira Saito4 ; Ingo Schiermeyer5 ; Masao Tsugaki6 ; Tomoki Yamashita7 ; Shuya Chiba ; Yoshimi Egawa ; Jun Fujisawa ; Akira Saito ; Ingo Schiermeyer ; Masao Tsugaki ; Tomoki Yamashita
1Applied Mathematics, Faculty of Advanced Science and Technology, Kumamoto University, Kumamoto, Japan
2Department of Applied Mathematics, Tokyo University of Science, Tokyo, Japan
3Faculty of Business and Commerce, Keio University, Yokohama, Japan
4Department of Information Science, Nihon University, Tokyo, Japan
5Institut für Diskrete Mathematik und Algebra, Technische Universität Bergakad-emie Freiberg, Freiberg, Germany
6Tokyo University of Science, Tokyo, Japan
7Department of Mathematics, Kindai University, Osaka, Japan
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 541-546 
Shuya Chiba; Yoshimi Egawa; Jun Fujisawa; Akira Saito; Ingo Schiermeyer; Masao Tsugaki; Tomoki Yamashita; Shuya Chiba; Yoshimi Egawa; Jun Fujisawa; Akira Saito; Ingo Schiermeyer; Masao Tsugaki; Tomoki Yamashita. On 2-factors with a specified number of components in line graphs. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 541-546. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a29/
@article{AMUC_2019_88_3_a29,
     author = {Shuya Chiba and Yoshimi Egawa and Jun Fujisawa and Akira Saito and Ingo Schiermeyer and Masao Tsugaki and Tomoki Yamashita and Shuya Chiba and Yoshimi Egawa and Jun Fujisawa and Akira Saito and Ingo Schiermeyer and Masao Tsugaki and Tomoki Yamashita},
     title = { On 2-factors with a specified number of components in line graphs},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {541--546},
     year = {2019},
     volume = {88},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a29/}
}
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%A Masao Tsugaki
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%A Shuya Chiba
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%A Jun Fujisawa
%A Akira Saito
%A Ingo Schiermeyer
%A Masao Tsugaki
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Voir la notice de l'article provenant de la source Comenius University

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.