Geodesic
Strong Tutte Type Conditions and Factors of Graphs
Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 4, pp. 1057-1065.

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Let odd(G) denote the number of odd components of a graph G and k ≥ 2 be an integer. We give sufficient conditions using odd(G − S) for a graph G to have an even factor. Moreover, we show that if a graph G satisfies odd(G − S) ≤ max1, (1/k)|S| for all S ⊂ V (G), then G has a (k − 1)-regular factor for k ≥ 3 or an H-factor for k = 2, where we say that G has an H-factor if for every labeling h : V (G) → red, blue with #v ∈ V (G) : f(v) = red even, G has a spanning subgraph F such that degF (x) = 1 if h(x) = red and degF (x) ∈ 0, 2 otherwise.
Keywords: factor of graph, even factor, regular factor, Tutte type condition 
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Yan, Zheng; Kano, Mikio. Strong Tutte Type Conditions and Factors of Graphs. Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 4, pp. 1057-1065. http://geodesic.mathdoc.fr/item/DMGT_2020_40_4_a7/

[1] A. Amahashi, On factors with all degrees odd, Graphs Combin. 1 (1985) 111–114. doi:10.1007/BF02582935

[2] A. Amahashi and M. Kano, On factors with given components, Discrete Math. 42 (1982) 1–6. doi:10.1016/0012-365X(82)90048-6

[3] J. Akiyama and M. Kano, Factors and Factorizations of Graphs, in: Lecture Notes in Math. 2031, (Springer-Verlag, Berlin 2011). doi:10.1007/978-3-642-21919-1

[4] Y. Cui and M. Kano, Some results on odd factors of graphs, J. Graph Theory 12 (1988) 327–333. doi:10.1002/jgt.3190120305

[5] H. Enomoto, B. Jackson, P. Katerinis and A. Saito, Toughness and the existence of k-factors, J. Graph Theory 9 (1985) 87–95. doi:10.1002/jgt.3190090106

[6] M. Kano, H. Lu and Q. Yu, Components factors with large components in graphs, Appl. Math. Lett. 23 (2010) 385–389. doi:10.1016/j.aml.2009.11.003

[7] M. Kano and A. Saito, Star-factors with large components, Discrete Math. 312 (2012) 2005–2008. doi:10.1016/j.disc.2012.03.017

[8] M. Las Vergnas, An extension of Tutte’s 1 -factor theorem, Discrete Math. 23 (1978) 241–255. doi:10.1016/0012-365X(78)90006-7

[9] H. Lu and M. Kano, Characterization of 1 -tough graphs using factors (2017). arXiv:1702.05873

[10] H. Lu and D. Wang, On Cui-Kano’s characterization problem on graph factors, J. Graph Theory 74 (2013) 335–343. doi:10.1002/jgt.21712

[11] L. Lovász, Combinatorial Problems and Exercises (North-Holland, Amsterdam, 1979). doi:10.1016/C2009-0-09109-0

[12] W.T. Tutte, The factorization of linear graphs, J. Lond. Math. Soc. (2) 22 (1947) 107–111. doi:10.1112/jlms/s1-22.2.107

[13] W.T. Tutte, The 1 -factors of oriented graphs, Proc. Amer. Math. Soc. 4 (1953) 922–931. doi:10.2307/2031831

[14] D. West, Introduction to Graph Theory (Prentice Hall, 1996).

[15] Y. Zhang, G. Yan and M. Kano, Star-like factors with large components, J. Oper. Res. Soc. China 3 (2015) 81–88. doi:10.1007/s40305-014-0066-7