TITLE: What was Smith's proof of Smith's theorem on Hamilton cycles in cubic graphs?
QUESTION [13 upvotes]: 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?

REPLY [2 votes]: 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.