**Supplemental material for “Tropically planar graphs”:**

This text file has all 151 tropically planar graphs of genus 6. They are sorted by their numbers of loops and biedges. Each graph entry is written as [n](B,L){…}, where n is an integer, B is the number of biedges, and L is the number of loops. The list {…} contains all edges in the graph. For example, the entry

[10](1, 0){{6,10},{6,10},{6,7},{7,11},{7,12},{10,11},{11,12},{12,13},{13,14},{13,23},{14,24},{14,22},{22,24},{22,23},{23,24}}

corresponds to the following graph, which has 1 biedge and 0 loops. (There is no particular significance to the names of the vertices.)

This text file has all 672 tropically planar graphs of genus 7. The notation is the same as for genus 6.