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September 16, 2022

MTSU/Vanderbilt Graph Theory and Combinatorics Seminar-Vanderbilt: 206 Buttrick Hall- Orientable embeddings with eulerian faces

Embeddings with faces bounded by euler circuits arise in several situations, such as building DNA models of graphs that can be scanned easily, and finding maximum genus orientable directed embeddings of digraphs.  We discuss results on the existence of such embeddings.  First, graphs where all vertices have degree congruent to 2 mod 4 have an orientable embedding with two euler circuit faces.  Second, n-vertex eulerian graphs where all vertices have at least (4n+2)/5 distinct neighbours also have such an embedding.  We discuss some of the ideas used in the proofs of these results and some extensions and related results. This is joint work with Jo Ellis-Monaghan.