摘要
Let G be a connected general graph. For any vertex v ∈ V (G) and any function f : V(G) → Z+, we introduce a set J∗f (v) consisting of the integer f(v) and all odd integers less than f(v), including all negative odd integers. In this paper, we shows that the graph G satisfies the general Tutte-type condition o(G - S) ≤ ∑v∈S f(v) for any nonempty set S ⊃ V (G) if and only if either G has a colored J∗f-factor for any 2-end-coloring, or G is of odd order and is J∗f-critical for any 2-end-coloring. This characterization solves a problem posed by Akiyama and Kano, as well as a problem of Cui and Kano's.
源语言 | 英语 |
---|---|
页(从-至) | 1149-1159 |
页数 | 11 |
期刊 | SIAM Journal on Discrete Mathematics |
卷 | 31 |
期 | 2 |
DOI | |
出版状态 | 已出版 - 2017 |
指纹
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Lu, H., & Wang, D. G. L. (2017). A Tutte-type characterization for graph factors. SIAM Journal on Discrete Mathematics, 31(2), 1149-1159. https://doi.org/10.1137/16M1079609