Let $M$ be a 2-dimensional closed Riemmanian manifold diffeomorphic to $S^2$.

S.B.Myers says "the cut-locus of every point $x\in M$ is a finite tree."

1. How the set of point can be a tree? What are the edges?
2. Is $p$ an element of $\operatorname{cut-locus}(p)$?

I can not find any paper of Myers in this case. Thanks!