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author:

Jiang, H. (Jiang, H..) [1] | Yang, D. (Yang, D..) [2]

Indexed by:

Scopus

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.

Keyword:

Community:

  • [ 1 ] [Jiang, H.]Center for Discrete Mathematics, Fuzhou University, Fuzhou, Fujian, 350003, China
  • [ 2 ] [Yang, D.]Center for Discrete Mathematics, Fuzhou University, Fuzhou, Fujian, 350003, China

Reprint 's Address:

  • [Jiang, H.]Center for Discrete Mathematics, Fuzhou UniversityChina

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Source :

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:

WoS CC Cited Count:

SCOPUS Cited Count: 12

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 0

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