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Abstract:
The fractional arboricity of a graph G, denoted by γf(G), is defined as γf(G)=maxH⊆G,v(H)>1[Formula presented]. The famous Nash–Williams Theorem states that a graph G can be partitioned into at most k forests if and only if γf(G)≤k. A graph is d-bounded if it has maximum degree at most d. The Nine Dragon Tree (NDT) Conjecture [posed by Montassier, Ossona de Mendez, Raspaud, and Zhu, at [11]] asserts that if γf(G)≤k+[Formula presented], then G decomposes into k+1 forests with one being d-bounded. In this paper, it is proven that the Nine Dragon Tree Conjecture is true for all the cases in which d=1. © 2018 Elsevier Inc.
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Journal of Combinatorial Theory. Series B
ISSN: 0095-8956
Year: 2018
Volume: 131
Page: 40-54
0 . 8 9 2
JCR@2018
1 . 2 0 0
JCR@2023
ESI HC Threshold:68
JCR Journal Grade:2
CAS Journal Grade:2
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ESI Highly Cited Papers on the List: 0 Unfold All
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30 Days PV: 1
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