과제정보
This work was financially supported by NRF 2020R1I1A1A0105858711. This work was financially supported by NRF 2020R1F1A1A01048226, NRF 2021K2A9A2A06044515, and NRF 2021K2A9A2A1110161711.
참고문헌
- B. Bollobas, A. Saito, and N. C. Wormald, Regular factors of regular graphs, J. Graph Theory 9 (1985), no. 1, 97-103. https://doi.org/10.1002/jgt.3190090107
- E.-K. Cho, J. Y. Hyun, S. O, and J. R. Park, Sharp conditions for the existence of an even [a, b]-factor in a graph, Bull. Korean Math. Soc. 58 (2021), no. 1, 31-46. https://doi.org/10.4134/BKMS.b191050
- H. Fleischner, Spanning Eulerian subgraphs, the splitting lemma, and Petersen's theorem, Discrete Math. 101 (1992), no. 1-3, 33-37. https://doi.org/10.1016/0012-365X(92)90587-6
- T. Gallai, On factorisation of graphs, Acta Math. Acad. Sci. Hungar. 1 (1950), 133-153. https://doi.org/10.1007/BF02022560
- X. Gu, Regular factors and eigenvalues of regular graphs, European J. Combin. 42 (2014), 15-25. https://doi.org/10.1016/j.ejc.2014.05.007
- D. Kim and S. O, Eigenvalues and parity factors in graphs, preprint.
- S. Kim, S. O, J. Park, and H. Ree, An odd [1, b]-factor in regular graphs from eigenvalues, Discrete Math. 343 (2020), no. 8, 111906, 4 pp. https://doi.org/10.1016/j.disc.2020.111906
- M. Kouider and P. D. Vestergaard, On even [2, b]-factors in graphs, Australas. J. Combin. 27 (2003), 139-147.
- M. Kouider and P. D. Vestergaard, Even [a, b]-factors in graphs, Discuss. Math. Graph Theory 24 (2004), no. 3, 431-441. https://doi.org/10.7151/dmgt.1242
- H. Liu and H. Lu, A degree condition for a graph to have (a, b)-parity factors, Discrete Math. 341 (2018), no. 1, 244-252. https://doi.org/10.1016/j.disc.2017.08.035
- L. Lovasz, The factorization of graphs. II, Acta Math. Acad. Sci. Hungar. 23 (1972), no. 1-2, 223-246. https://doi.org/10.1007/BF01889919
- H. Lu, Regular graphs, eigenvalues and regular factors, J. Graph Theory 69 (2012), no. 4, 349-355. https://doi.org/10.1002/jgt.20581
- H. Lu, Z. Wu, and X. Yang, Eigenvalues and [1, n]-odd factors, Linear Algebra Appl. 433 (2010), no. 4, 750-757. https://doi.org/10.1016/j.laa.2010.04.002
- H. Matsuda, Ore-type conditions for the existence of even [2, b]-factors in graphs, Discrete Math. 304 (2005), no. 1-3, 51-61. https://doi.org/10.1016/j.disc.2005.09.009
- S. O, Eigenvalues and [a, b]-factors in regular graphs, J. Graph Theory (published online) https://doi.org/10.1002/jgt.22789
- S. O and D. B. West, Matching and edge-connectivity in regular graphs, European J. Combin. 32 (2011), no. 2, 324-329. https://doi.org/10.1016/j.ejc.2010.10.005
- O. Ore, Note on Hamilton circuits, Amer. Math. Monthly 67 (1960), 55. https://doi.org/10.2307/2308928
- D. B. West, Introduction to Graph Theory, Prentice Hall, Inc., Upper Saddle River, NJ, 1996.