Is there a formula for the genus of a bipartite graph with 2 sets of m vertices, where each vertex has order 3? I.e. if m=3 this is K(3,3). But I'm interested in larger m.
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I'm sure it depends on which such graph you're looking at. E.g., you could just have a union of several copies of $K_{3,3}$, which would have genus one. – Gerry Myerson Sep 11 '19 at 23:31
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The Desargues graph https://en.wikipedia.org/wiki/Desargues_graph for example has genus two. – Gerry Myerson Sep 11 '19 at 23:43
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Care to interact with the comments, Tony? – Gerry Myerson Sep 13 '19 at 13:05
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I should have added "connected" to the specs. The Desargues graph does – Tony Phillips Sep 13 '19 at 15:52
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not look bipartite to me. Am I missing something? – Tony Phillips Sep 13 '19 at 15:53
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Now I understand your point. I misinterpreted "Let G(n, d) denote a connected regular bipartite graph on 2n vertices and of degree d. " as implying that there – Tony Phillips Sep 13 '19 at 19:58
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was only one. My question probably doesn't make sense. Sorry. – Tony Phillips Sep 13 '19 at 19:58
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Well, it says at the Wikipedia link that it's bipartite. Try labeling the vertices alternately A and B, and I think you'll find that no two vertices with the same label are adjacent. – Gerry Myerson Sep 13 '19 at 22:35