Nowhere-zero flows on 2-edge-connected graphs can be reconfigured via successive cycle changes for Z_2^8-flows and sufficiently large groups, but the 5-flow reconfiguration conjecture is false, with group structure mattering unlike existence.
Recoloring planar graphs of girth at least five.SIAM J
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Nowhere-zero flow reconfiguration
Nowhere-zero flows on 2-edge-connected graphs can be reconfigured via successive cycle changes for Z_2^8-flows and sufficiently large groups, but the 5-flow reconfiguration conjecture is false, with group structure mattering unlike existence.