Nowhere-zero 3-flows in toroidal graphs

2022 ◽  
Vol 153 ◽  
pp. 61-80
Author(s):  
Jiaao Li ◽  
Yulai Ma ◽  
Zhengke Miao ◽  
Yongtang Shi ◽  
Weifan Wang ◽  
...  
Keyword(s):  
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.

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

Edge Partition of Toroidal Graphs into Forests in Linear Time

2005 ◽  
Vol 22 ◽  
pp. 421-425 ◽  
Author(s):  
Nicolas Bonichon ◽  
Cyril Gavoille ◽  
Arnaud Labourel
Keyword(s):  
Linear Time ◽  
Toroidal Graphs ◽  
Edge Partition

On edge colorings of 1-toroidal graphs

2013 ◽  
Vol 29 (7) ◽  
pp. 1421-1428
Author(s):  
Xin Zhang ◽  
Gui Zhen Liu
Keyword(s):  
Edge Colorings ◽  
Toroidal Graphs

Linear 2-Arboricity of Toroidal Graphs

2016 ◽  
Vol 41 (4) ◽  
pp. 1907-1921 ◽  
Author(s):  
Weifan Wang ◽  
Yuanchao Li ◽  
Xiaoxue Hu ◽  
Yiqiao Wang
Keyword(s):  
Toroidal Graphs

5-Connected Toroidal Graphs are Hamiltonian-Connected

2016 ◽  
Vol 30 (1) ◽  
pp. 112-140 ◽  
Author(s):  
Ken-ichi Kawarabayashi ◽  
Kenta Ozeki
Keyword(s):  
Hamiltonian Connected ◽  
Toroidal Graphs

scholarly journals Decomposing toroidal graphs into circuits and edges

2005 ◽  
Vol 148 (2) ◽  
pp. 147-159 ◽  
Author(s):  
Baogang Xu ◽  
Lusheng Wang
Keyword(s):  
Toroidal Graphs

scholarly journals Hamilton paths in toroidal graphs

2005 ◽  
Vol 94 (2) ◽  
pp. 214-236 ◽  
Author(s):  
Robin Thomas ◽  
Xingxing Yu ◽  
Wenan Zang
Keyword(s):  
Toroidal Graphs ◽  
Hamilton Paths
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