Wolfram Tech Support has confirmed a bug in FindHamiltonianPath that affects Mathematica 11.3.0 under Windows 10. I reported it when the function would sometimes cause the kernel to quit. The function usually works fine.
When weighted graph G causes the function to fail on my Windows machine, I simply run FindHamiltonianPath@G in MathematicaOnline to get an answer (or a friend runs it on his Mac). The offending weighted graphs seem perfectly normal (unfortunately, I cannot post the geolocation data used to build the graphs).
Has anyone encountered this problem under Windows and if so, did you find a workaround? Thanks.