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Results tagged with hamiltonian-graphs
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user 1492
A Hamiltonian graph (directed or undirected) is a graph that contains a Hamiltonian cycle, that is, a cycle that visits every vertex exactly once.
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Is there a non-bipartite hamiltonian cubic graph on $n$ vertices with no $(n-1)$-cycle?
Is there a cubic (3-regular) graph $G$ on $n$ vertices such that:
$G$ is hamiltonian
$G$ has no $(n-1)$-cycles
$G$ is not bipartite
My computer tells me that there are none on up to $24$ vertices …
- 12.7k
9
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Heuristic arguments regarding Sheehan's conjecture?
Sheehan conjectured that there are no 4-regular graphs that are uniquely hamiltonian (i.e. have exactly one hamilton cycle).
Evidence that might be loosely seen to be in favour of this conjecture is: …
- 12.7k
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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 …
- 12.7k
6
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Minimum number of hamilton cycles in a 4-connected planar triangulation?
I am currently interested in hamilton cycles (i.e. a cycle through every vertex) in planar triangulations (i.e. planar graphs with every face a triangle).
There are non-hamiltonian planar triangulati …
- 12.7k
7
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1
answer
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Grinberg's uniquely hamiltonian 3-connected graphs (Russian paper)
Many years ago, Grinberg found some uniquely-hamiltonian $3$-connected graphs, and published his results in a paper that has been cited several times as follows.
E. Grinberg, Three-connected graph …
- 12.7k
15
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answers
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What is the smallest uniquely hamiltonian graph with minimum degree at least 3?
I would like to know more about uniquely hamiltonian graphs with minimum vertex degree at least 3, and in particular what is the smallest one.
(Recall that a graph is hamiltonian if it has a cycle pas …
- 12.7k
14
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What was Smith's proof of Smith's theorem on Hamilton cycles in cubic graphs?
In a short 1946 paper "On Hamiltonian Circuits", Tutte proved the famous result that an edge in a cubic graph lies in an even number of Hamilton circuits.
He attributed the result to his friend CAB S …
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