2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228565The mapping class group of a genus $g$ surface $Σ_{g,1}$ with one boundary component is known to have a simple yet infinite presentation with generators given by elementary moves called Whitehead moves on so-called marked bordered fatgraphs. In this paper, we introduce an algorithm called "fatgraph Nielsen reduction" which, from the action of a mapping class $φ\in MC_{g,1}$ of $Σ_{g,1}$ on the fundamental group $π_1(Σ_{g,1})$ of $Σ_{g,1}$, determines a sequence of Whitehead moves representing $φ$ beginning at any choice of marked bordered fatgraph. As a consequence, this leads to an algorithm which factors any mapping class given by its action on $π(Σ_{g,1})$ in terms of a certain generating set for $MC_{g,1}$.16 pages, 4 figuresGeometric Topology20F38; 05C25; 20F34; 57M99; 32G15; 20F05; 20F06; 20F99text