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Settling the nonorientable genus of the nearly complete bipartite graphs

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arxiv 2305.14048 v1 pith:GGQP62IK submitted 2023-05-23 math.CO

Warren Singh , Timothy Sun This is my paper
classification math.CO
keywords bipartitecompletegraphsgenuscasesgraphnearlynonorientable
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A graph is said to be nearly complete bipartite if it can be obtained by deleting a set of independent edges from a complete bipartite graph. The nonorientable genus of such graphs is known except in a few cases where the sizes of the partite classes differ by at most one, and a maximum matching is deleted. We resolve these missing cases using three classic tools for constructing genus embeddings of the complete bipartite graphs: current graphs, diamond sums, and the direct rotation systems of Ringel.

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