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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 Smith, but explicitly mentioned that the proof was not Smith's proof.

What was Smith's proof?

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    $\begingroup$ I find this a wonderful question, especially since it rests on an implicit assumption that proofs are mathematical objects and can be meaningfully non-isomorphic, a very important and modern topic. Tangentially relevant comments: (0) an article on the "CAB Smith" in the OP is this, (1) there should be people around who have known him personally, (2) the first constructive proof was given by Thomason via his 'lollipop-method', (3) the newest news on Smithian theorem is this preprint of Pitz. $\endgroup$ – Peter Heinig Aug 24 '17 at 14:15
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I am fairly sure that I once asked Adrian Bondy about it, who replied something along the lines of Bill Tutte having told him that the original proof by Smith was quite messy.

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  • $\begingroup$ Thanks Tommy...and welcome to MO. Given that there is an algebraic proof (Tutte's) and two constructive/algorithmic proofs (yours and Thomason's), I wonder if Smith's was again different. $\endgroup$ – Gordon Royle May 23 at 23:46

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