I care. I was a math student in my undergrad when I try to solve a particular problem on paths, in the end it uses a path version of cycle double cover conjecture (which was solved in the 90s).

https://chaoxu.prof/posts/2013-01-30-there-exist-a-path-of-l...

I also want to get it to work on cycles, but then I hit the cycle double cover conjecture so I gave up.