I have been digging on the internet for the proof of this theorem for
the last couple of days without success. The result was published by Sir
Crispin Nash-Williams as Valency Sequences which force graphs to have
Hamiltonian Circuits. Interim Rep, University of Waterloo Res Rep.,
Waterloo, Ontario, 1969. However …

A while back, Bob L. Sturm blogged about a similar implementation of
OMP to the one in scikit-learn. Instead of using the Cholesky
decomposition like we did, his Matlab code uses the QR decomposition, to
a similar (or maybe even identical) outcome, in theory. So lucky that
Alejandro pointed out …