Abstract

This thesis is devoted to finding a finite algorithm to
calculate the \emph{stable gonality} of graphs. The stable
gonality was first defined by Cornelissen et al. in
\cite{Gunther}. A \emph{finite harmonic morphism} $\vp$ is a
map from a refinement $H$ of a graph $G$ to a tree $T$ obeying
several properties. Together
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