# Which Cubic Graphs have Quadrangulated Spherical Immersions

@article{Abrams2019WhichCG, title={Which Cubic Graphs have Quadrangulated Spherical Immersions}, author={Lowell Abrams and Yosef Berman and Vance Faber and Michael Murphy}, journal={arXiv: Combinatorics}, year={2019} }

We consider spherical quadrangulations, i.e., graph embeddings in the sphere, in which every face has boundary walk of length 4, and all vertices have degree 3 or 4. Interpreting each degree 4 vertex as a crossing, these embeddings can also be thought of as transversal immersions of cubic graphs which we refer to as "the extracted graphs". We also consider quadrangulations of the disk in which interior vertices have degree 3 or 4 and boundary vertices have degree 2 or 3. First, we classify all…

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