H^*-Connected Graph
المؤلف:
Bryant, D. and Dean, M
المصدر:
"Vertex-Transitive Graphs that have no Hamilton Decomposition." 25 Aug 2014. http://arxiv.org/abs/1408.5211.
الجزء والصفحة:
...
11-5-2022
1187
H^*-Connected Graph
A graph is said to be 
-connected if it is either Hamilton-connected or Hamilton-laceable.
S. Wagon (pers. comm., May. 20, 2013; Dupuis and Wagon 2014) conjecture that all connected vertex-transitive graphs are 
-connected with the following exceptions: cycle graphs, the dodecahedral graph, Petersen graph, Coxeter graph, triangle-replaced Petersen graph, and triangle-replaced Coxeter graph. The conjecture can be restated as, "Every Hamiltonian vertex-transitive graph is 
-connected except cycle graphs 
for 
and the dodecahedral graph." It was been verified up to 
nodes.
REFERENCES
Bryant, D. and Dean, M. "Vertex-Transitive Graphs that have no Hamilton Decomposition." 25 Aug 2014. http://arxiv.org/abs/1408.5211.
Dupuis, M. and Wagon, S. "Laceable Knights." To appear in Ars Math Contemp.
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