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What is the correct way? Hamilton path, Hamilton's path or Hamiltonian path? To be clear, I am referring to the correct way to name a graph such that there exists a single path (without repeated vertices) through all the vertices.

In Wikipedia it says "Hamiltonian path", whereas in an article I found "Hamilton path".

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    $\begingroup$ I think you see all three used. I personally prefer "Hamiltonian path" for no specific reason. Pick a term, define it, and stick to it in your writing. $\endgroup$ – Juho Feb 15 '14 at 1:00
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    $\begingroup$ I have never seen Hamilton's path. The other two forms I have. $\endgroup$ – Yuval Filmus Feb 15 '14 at 3:28
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I have seen both Hamilton path (or Hamilton cycle) and Hamiltonian path (or Hamiltonian cycle). A graph, however, is always Hamiltonian (if it contains a Hamilton/Hamiltonian cycle). Consider for example the titles of two papers: Hamiltonian cycles in random regular graphs (Fenner & Frieze) and Generating and counting Hamilton cycles in random regular graphs (Frieze, Jerrum, Molloy, Robinson & Wormald). Alan Frieze apparently doesn't care too strongly about the issue.

However, I've never seen Hamilton's path or cycle.

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