Vertex-arboricity of toroidal graphs without K5− and 6-cycles

2022 ◽  
Vol 310 ◽  
pp. 97-108
Author(s):  
Aina Zhu ◽  
Dong Chen ◽  
Min Chen ◽  
Weifan Wang
Keyword(s):  
Vertex Arboricity ◽  
Toroidal Graphs

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

scholarly journals List vertex-arboricity of toroidal graphs without 4-cycles adjacent to 3-cycles

2016 ◽  
Vol 339 (10) ◽  
pp. 2526-2535 ◽  
Author(s):  
Min Chen ◽  
Li Huang ◽  
Weifan Wang
Keyword(s):  
Vertex Arboricity ◽  
Toroidal Graphs

scholarly journals Vertex arboricity of toroidal graphs with a forbidden cycle

2014 ◽  
Vol 333 ◽  
pp. 101-105 ◽  
Author(s):  
Ilkyoo Choi ◽  
Haihui Zhang
Keyword(s):  
Vertex Arboricity ◽  
Toroidal Graphs

Hamiltonicity of a class of toroidal graphs

2020 ◽  
Vol 70 (2) ◽  
pp. 497-503
Author(s):  
Dipendu Maity ◽  
Ashish Kumar Upadhyay
Keyword(s):  
Connected Graph ◽  
Hamiltonian Cycle ◽  
Partial Solution ◽  
The Other ◽  
Hamiltonian Cycles ◽  
The Face ◽  
Toroidal Graphs

Abstract If the face-cycles at all the vertices in a map are of same type then the map is said to be a semi-equivelar map. There are eleven types of semi-equivelar maps on the torus. In 1972 Altshuler has presented a study of Hamiltonian cycles in semi-equivelar maps of three types {36}, {44} and {63} on the torus. In this article we study Hamiltonicity of semi-equivelar maps of the other eight types {33, 42}, {32, 41, 31, 41}, {31, 61, 31, 61}, {34, 61}, {41, 82}, {31, 122}, {41, 61, 121} and {31, 41, 61, 41} on the torus. This gives a partial solution to the well known Conjecture that every 4-connected graph on the torus has a Hamiltonian cycle.

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 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
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