Abstract
The classical Gauss code problem asks to characterize which cyclic sequences arise as the vertex sequence of the ‘straight-ahead path of a 4-regular graph embedded in the plane This problem is generalized to certain 4 regular graphs in arbitrary surfaces
A characterization is given for the existence of a 4-regular graph in a specified surface yielding the specified sequence This characterization is obtained using a generalization of Shank's left-right paths
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Lins, S., Richtfr, B. & Shank, H. The Gauss code problem off the plane. Aeq. Math. 33, 81–95 (1987). https://doi.org/10.1007/BF01836154
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DOI: https://doi.org/10.1007/BF01836154