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

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.

scholarly journals Forbidden subgraphs of graphs uniquely Hamiltonian-connected from a vertex

1998 ◽  
Vol 187 (1-3) ◽  
pp. 281-290 ◽  
Author(s):  
George R.T. Hendry ◽  
C.J. Knickerbocker ◽  
Patti Frazer Lock ◽  
Michael Sheard
Keyword(s):  
Forbidden Subgraphs ◽  
Hamiltonian Connected

3-Connected {K 1,3, P 9}-Free Graphs are Hamiltonian-Connected

2013 ◽  
Vol 30 (5) ◽  
pp. 1099-1122 ◽  
Author(s):  
Qiuju Bian ◽  
Ronald J. Gould ◽  
Paul Horn ◽  
Susan Janiszewski ◽  
Steven La Fleur ◽  
...  
Keyword(s):  
Hamiltonian Connected

A note on locally connected and hamiltonian-connected graphs

1979 ◽  
Vol 33 (1) ◽  
pp. 5-8 ◽  
Author(s):  
Gary Chartrand ◽  
Ronald J. Gould ◽  
Albert D. Polimeni
Keyword(s):  
Connected Graphs ◽  
Hamiltonian Connected

Optimal Fault-Tolerant Hamiltonian and Hamiltonian Connected Graphs

2008 ◽  
Author(s):  
Y-Chuang Chen ◽  
Yong-Zen Huang ◽  
Lih-Hsing Hsu ◽  
Jimmy J. M. Tan ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Fault Tolerant ◽  
Connected Graphs ◽  
Hamiltonian Connected

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
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