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Abstract:
The fractional arboricity of a graph G, denoted by Γf (G), is defined asΓf(G)=maxH⊆G,v(H)>1e(H)v(H)−1. The celebrated Nash-Williams’ Theorem states that a graph G can be partitioned into at most k forests if and only if Γf (G)≤k. The Nine Dragon Tree (NDT) Conjecture [posed by Montassier, Ossona de Mendez, Raspaud, and Zhu, in “Decomposing a graph into forests”, J. Combin. Theory Ser. B 102 (2012) 38-52] asserts that if Γf(G)≤k+dk+d+1, then G decomposes into k+1 forests with one having maximum degree at most d. In this paper, we prove the Nine Dragon Tree (NDT) Conjecture. © 2016, János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg.
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Combinatorica
ISSN: 0209-9683
Year: 2017
Issue: 6
Volume: 37
Page: 1125-1137
1 . 4 0 6
JCR@2017
1 . 0 0 0
JCR@2023
ESI HC Threshold:71
JCR Journal Grade:1
CAS Journal Grade:2
Cited Count:
SCOPUS Cited Count: 12
ESI Highly Cited Papers on the List: 0 Unfold All
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30 Days PV: 0
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