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Date: 10-3-2022
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Date: 7-4-2022
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Date: 12-4-2022
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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.
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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