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2-factor; claw-free graph; line graph; $N^{2}$-locally connected

References:

[1] Bondy, J. A., Murty, U. S. R.: **Graph Theory with Applications**. American Elsevier Publishing Co. New York (1976). MR 0411988

[2] Choudum, S. A., Paulraj, M. S.: **Regular factors in $K_{1, 3}$-free graphs**. J. Graph Theory 15 (1991), 259-265. DOI 10.1002/jgt.3190150304 | MR 1111989

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[4] Gould, R. J., Hynds, E. A.: **A note on cycles in 2-factors of line graphs**. Bull. Inst. Comb. Appl. 26 (1999), 46-48. MR 1683819 | Zbl 0922.05046

[5] Li, G., Liu, Z.: **On 2-factors in claw-free graphs**. Syst. Sci. Math. Sci. 8 (1995), 369-372. MR 1374533 | Zbl 0851.05084

[6] Ryjáček, Z.: **On a closure concept in claw-free graphs**. J. Comb. Theory, Ser. B 70 (1997), 217-224. DOI 10.1006/jctb.1996.1732 | MR 1459867

[7] Ryjáček, Z., Saito, A., Schelp, R. H.: **Closure, 2-factors, and cycle coverings in claw-free graphs**. J. Graph Theory 32 (1999), 109-117. DOI 10.1002/(SICI)1097-0118(199910)32:2<109::AID-JGT1>3.0.CO;2-O | MR 1709653 | Zbl 0932.05045

[8] Tian, R., Xiong, L., Niu, Z.: **On 2-factors in claw-free graphs whose edges are in small cycles**. Discrete Math. 312 (2012), 3140-3145. DOI 10.1016/j.disc.2012.07.005 | MR 2957934 | Zbl 1251.05145

[9] Yoshimoto, K.: **On the number of components in 2-factors of claw-free graphs**. Discrete Math. 307 (2007), 2808-2819. DOI 10.1016/j.disc.2006.11.022 | MR 2362964 | Zbl 1129.05037