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Is this case of Barnette's Conjecture known?

Context: Barnette's Conjecture is that every bipartite cubic polyhedral graph is Hamiltonian. I have been interested by this problem for a long time, and I recently came up with a result. From my ...
Zach Hunter's user avatar
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4 votes
0 answers
99 views

Maximal non-hamiltonian graphs - spanned by a theta graph?

At the moment I am interested in maximal non-hamiltonian graphs, so that is a (simple, undirected) graph that does not itself have a hamilton cycle, but if you add an edge between any two distinct non-...
Gordon Royle's user avatar
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3 votes
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Reference request: Bipartite symmetric graphs are hamiltonian

Does anyone know whether bipartite symmetric graphs are hamiltonian? I'm not sure whether anyone have proved it before, but a nonhamiltonian symmetric bipartite graph would lead to a counterexample to ...
LeechLattice's user avatar
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86 views

Uniqueness of compatible cycle decomposition for Eulerian trail

Fleischner mentions in his article Uniqueness of maximal dominating cycles in 3-regular graphs and of hamiltonian cycles in 4-regular graphs about the uniqueness of compatible cycle decomposition that ...
False Equivalence's user avatar