Geodesic
Strong ƒ-Star Factors of Graphs
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 3, pp. 475-482.

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Let G be a graph and f : V (G) → 2, 3, . . .. A spanning subgraph F is called strong f-star of G if each component of F is a star whose center x satisfies degF (x) ≤ ƒ(x) and F is an induced subgraph of G. In this paper, we prove that G has a strong f-star factor if and only if oddca(G − S) ≤ ∑x∊S ƒ(x) for all S ⊂ V (G), where oddca(G) denotes the number of odd complete-cacti of G.
Keywords: ƒ-star factor, strong ƒ-star factor, complete-cactus, factor of graph 
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Yan, Zheng. Strong ƒ-Star Factors of Graphs. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 3, pp. 475-482. http://geodesic.mathdoc.fr/item/DMGT_2015_35_3_a6/

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