Spanning path-cycle systems with given end-vertices in regular graphs (full version)

Yoshimi Egawa, Mikio Kano, Kenta Ozeki

We prove the following theorem. Let $r\ge 4$ be an integer, and $G$ be a $K_{1,r}$-free $r$-edge-connected $r$-regular graph. Then, for every set $W$ of even number of vertices of…