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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     title = {Strong {Tutte} {Type} {Conditions} and {Factors} of {Graphs}},
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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/