Effective divisor classes on metric graphs

We introduce the notion of semibreak divisors on metric graphs and prove that every effective divisor class (of degree at most genus) has a representative. This appropriately generalizes break (in equal to genus). provide an algorithm efficiently compute such representatives. Semibreak tool establish some basic properties loci inside Picard groups graphs. are pure-dimensional polyhedral sets. also ‘generic’ rank zero, Abel-Jacobi map is ‘birational’ onto its image. These analogues classical results for Riemann surfaces.