Clifford’s Theorem for graphs

Abstract

Abstract Let Γ be a metric graph of genus g and let r be an integer with 2 ≤ r ≤ g − 2 such that Γ has a linear system g 2 r r $g_{2r}^r$ . Then Γ has a linear system g 2 1 $g_{2}^1$ . For algebraic curves this is part of Clifford’s well-known Theorem.