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Associated to every state surface for a knot or link is a state graph, whichembeds as a spine of the state surface. A state graph can be decomposed alongcut-vertices into graphs with induced planar embeddings. Associated with eachsuch planar graph is a checkerboard surface, and each state surface is a fiberif and only if all of its associated checkerboard surfaces are fibers. We givean algebraic condition that characterizes which checkerboard surfaces arefibers directly from their state graphs. We use this to classify fibering ofcheckerboard surfaces for several families of planar graphs, including thoseassociated with 2-bridge links. This characterizes fibering for many familiesof state surfaces.

State graphs and fibered state surfaces