A Mechanized Proof of the Max-Flow Min-Cut Theorem for Countable Networks

Andreas Lochbihler, Liron Cohen, Cezary Kaliszyk
2021
Aharoni et al. [Ron Aharoni et al., 2010] proved the max-flow min-cut theorem for countable networks, namely that in every countable network with finite edge capacities, there exists a flow and a cut such that the flow saturates all outgoing edges of the cut and is zero on all incoming edges. In this paper, we formalize their proof in Isabelle/HOL and thereby identify and fix several problems with their proof. We also provide a simpler proof for networks where the total outgoing capacity of all
more » ... vertices other than the source is finite. This proof is based on the max-flow min-cut theorem for finite networks.
doi:10.4230/lipics.itp.2021.25 fatcat:eonhznahkzcg3nrl6pwn7yr4ay