scholarly journals Rings whose total graphs have small vertex-arboricity and arboricity

2020 ◽  
pp. 1-10
Author(s):  
Kazem KHASHYARMANESH ◽  
Abbas MOHAMMADİAN
Keyword(s):  
Vertex Arboricity

Strong Equitable Vertex Arboricity in Cartesian Product Networks

2021 ◽  
pp. 2150010
Author(s):  
Zhiwei Guo ◽  
Yaping Mao ◽  
Nan Jia ◽  
He Li
Keyword(s):  
Maximum Degree ◽  
Cartesian Product ◽  
Color Class ◽  
Vertex Arboricity

An equitable [Formula: see text]-tree-coloring of a graph [Formula: see text] is defined as a [Formula: see text]-coloring of vertices of [Formula: see text] such that each component of the subgraph induced by each color class is a tree of maximum degree at most [Formula: see text], and the sizes of any two color classes differ by at most one. The strong equitable vertex [Formula: see text]-arboricity of a graph [Formula: see text] refers to the smallest integer [Formula: see text] such that [Formula: see text] has an equitable [Formula: see text]-tree-coloring for every [Formula: see text]. In this paper, we investigate the Cartesian product with respect to the strong equitable vertex [Formula: see text]-arboricity, and demonstrate the usefulness of the proposed constructions by applying them to some instances of product networks.

Vertex arboricity of planar graphs without intersecting 5-cycles

2017 ◽  
Vol 35 (2) ◽  
pp. 365-372 ◽  
Author(s):  
Hua Cai ◽  
Jianliang Wu ◽  
Lin Sun
Keyword(s):  
Planar Graphs ◽  
Vertex Arboricity

scholarly journals Equitable vertex arboricity of subcubic graphs

2016 ◽  
Vol 339 (6) ◽  
pp. 1724-1726 ◽  
Author(s):  
Xin Zhang
Keyword(s):  
Vertex Arboricity ◽  
Subcubic Graphs

scholarly journals Vertex arboricity of integer distance graph G(Dm,k)

2009 ◽  
Vol 309 (6) ◽  
pp. 1649-1657 ◽  
Author(s):  
Lian-Cui Zuo ◽  
Qinglin Yu ◽  
Jian-Liang Wu
Keyword(s):  
Distance Graph ◽  
Vertex Arboricity

A note on the list vertex arboricity of toroidal graphs

2018 ◽  
Vol 341 (12) ◽  
pp. 3344-3347
Author(s):  
Yiqiao Wang ◽  
Min Chen ◽  
Weifan Wang
Keyword(s):  
Vertex Arboricity ◽  
Toroidal Graphs

A note of vertex arboricity of planar graphs without 4-cycles intersecting with 6-cycles

2020 ◽  
Vol 836 ◽  
pp. 53-58
Author(s):  
Xuyang Cui ◽  
Wenshun Teng ◽  
Xing Liu ◽  
Huijuan Wang
Keyword(s):  
Planar Graphs ◽  
Vertex Arboricity

scholarly journals On the vertex-arboricity ofK5-minor-free graphs of diameter 2

2014 ◽  
Vol 322 ◽  
pp. 1-4 ◽  
Author(s):  
Fei Huang ◽  
Xiumei Wang ◽  
Jinjiang Yuan
Keyword(s):  
Vertex Arboricity ◽  
Minor Free Graphs

Equitable vertex arboricity of 5-degenerate graphs

2016 ◽  
Vol 34 (2) ◽  
pp. 426-432 ◽  
Author(s):  
Guantao Chen ◽  
Yuping Gao ◽  
Songling Shan ◽  
Guanghui Wang ◽  
Jianliang Wu
Keyword(s):  
Vertex Arboricity

scholarly journals Equitable list vertex colourability and arboricity of grids

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6353-6374 ◽  
Author(s):  
Ewa Drgas-Burchardt ◽  
Janusz Dybizbański ◽  
Hanna Furmańczyk ◽  
Elżbieta Sidorowicz
Keyword(s):  
General Graph ◽  
Acyclic Graph ◽  
Colour Class ◽  
Vertex Arboricity ◽  
General Graphs

A graph G is equitably k-list arborable if for any k-uniform list assignment L, there is an equitable L-colouring of G whose each colour class induces an acyclic graph. The smallest number k admitting such a coloring is named equitable list vertex arboricity and is denoted by ?=l (G). Zhang in 2016 posed the conjecture that if k ? ?(?(G) + 1)/2? then G is equitably k-list arborable. We give some new tools that are helpful in determining values of k for which a general graph is equitably k-list arborable. We use them to prove the Zhang?s conjecture for d-dimensional grids where d 2 {2,3,4} and give new bounds on ?=l (G) for general graphs and for d-dimensional grids with d ? 5.

scholarly journals Equitable Vertex Arboricity Conjecture Holds for Graphs with Low Degeneracy

2021 ◽  
Vol 37 (8) ◽  
pp. 1293-1302
Author(s):  
Xin Zhang ◽  
Bei Niu ◽  
Yan Li ◽  
Bi Li
Keyword(s):  
Vertex Arboricity
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