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author:

Yang, D. (Yang, D..) [1]

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Scopus

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.

Keyword:

Arboricity; Decomposition of a graph; Fractional arboricity; Graph; Nine Dragon Tree (NDT) Conjecture

Community:

  • [ 1 ] [Yang, D.]Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, China
  • [ 2 ] [Yang, D.]Center for Discrete Mathematics, Fuzhou University, Fuzhou, Fujian, China

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Source :

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

Cited Count:

WoS CC Cited Count:

SCOPUS Cited Count:

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 1

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