Graph Pebbling: A Blend of Graph Theory, Number Theory, and Optimization

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Abstract

DOI: https://doi.org/10.1090/noti2379 For example, in network optimization, one moves packages from supplies at some vertices to demands at others, with costs accrued per package across edges, attempting to do so most cheaply. In network flow, one tries to maximize the amount of material that can move from a source to a sink, subject to the capacities along edges and the conservation of flow at other vertices along the way. In various versions of pursuit and evasion, cops and robbers take turns moving along edges with the cops trying to capture robbers by landing on them; one tries to minimize the number of cops necessary to always capture the robbers. Zero forcing, black pebbling, chip firing, black and white