Clifford's Theorem for graphs

Abstract

Let $\Gamma$ be a metric graph having a linear system $g_{2r}^r$ for some $2\le r\le g-2$ then $\Gamma$ has a linear system $g_2^1$. This is similar to the well-known Clifford's Theorem from the theory of linear systems on smooth projective curves.

11 pages, 3 figures