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

Min Chen; Li Huang; Weifan Wang

doi:10.1016/j.disc.2016.04.010

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

Discrete Mathematics ◽

10.1016/j.disc.2016.04.010 ◽

2016 ◽

Vol 339 (10) ◽

pp. 2526-2535 ◽

Cited By ~ 3

Author(s):

Min Chen ◽

Li Huang ◽

Weifan Wang

Keyword(s):

Vertex Arboricity ◽

Toroidal Graphs

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A note on the list vertex arboricity of toroidal graphs

Discrete Mathematics ◽

10.1016/j.disc.2018.08.021 ◽

2018 ◽

Vol 341 (12) ◽

pp. 3344-3347

Author(s):

Yiqiao Wang ◽

Min Chen ◽

Weifan Wang

Keyword(s):

Vertex Arboricity ◽

Toroidal Graphs

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Vertex arboricity of toroidal graphs with a forbidden cycle

Discrete Mathematics ◽

10.1016/j.disc.2014.06.011 ◽

2014 ◽

Vol 333 ◽

pp. 101-105 ◽

Cited By ~ 3

Author(s):

Ilkyoo Choi ◽

Haihui Zhang

Keyword(s):

Vertex Arboricity ◽

Toroidal Graphs

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A note on vertex arboricity of toroidal graphs without 7-cycles

International Mathematical Forum ◽

10.12988/imf.2016.6672 ◽

2016 ◽

Vol 11 ◽

pp. 679-686

Author(s):

Haihui Zhang

Keyword(s):

Vertex Arboricity ◽

Toroidal Graphs

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

Discrete Applied Mathematics ◽

10.1016/j.dam.2021.12.020 ◽

2022 ◽

Vol 310 ◽

pp. 97-108

Author(s):

Aina Zhu ◽

Dong Chen ◽

Min Chen ◽

Weifan Wang

Keyword(s):

Vertex Arboricity ◽

Toroidal Graphs

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Hamiltonicity of a class of toroidal graphs

Mathematica Slovaca ◽

10.1515/ms-2017-0367 ◽

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.

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Strong Equitable Vertex Arboricity in Cartesian Product Networks

Journal of Interconnection Networks ◽

10.1142/s0219265921500109 ◽

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.

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