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math.CO2019
Which Cubic Graphs have Quadrangulated Spherical Immersions?
Lowell Abrams, Yosef Berman, Vance Faber +1
We consider spherical quadrangulations -- spherical embeddings of multigraphs, possibly with loops, so that every face has boundary walk of length 4 -- in which all vertices have d…
math.CO2019★ 1 cited
A Basic Structure for Grids in Surfaces
Lowell Abrams, Daniel Slilaty
A graph embedded in a surface is called an -grid when every facial boundary walk has length four, that is, the topological dual graph of in is 4-regular. Aside f…
math.CO2019★ 2 cited
New Dualities From Old: generating geometric, Petrie, and Wilson dualities and trialites of ribbon graphs
Lowell Abrams, Jo Ellis-Monaghan
We develop an algebraic framework for ribbon graphs, revealing symmetry properties of (partial) twisted duality. The original ribbon group action of Ellis-Monaghan and Moffatt rest…