What is the genus of this complete $4-$partite graph, $K_{m,2,2,2}$, where $m \in \mathbb{N}$?
Thanks in advance.
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$\begingroup$ Perhaps try math.stackexchange.com :-) Good luck $\endgroup$– David Roberts ♦Feb 18, 2014 at 6:44
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$\begingroup$ @DavidRoberts There is a similar questions in math.stackexchange.com, see math.stackexchange.com/questions/503277/…, but it has no answer. By the way, thank you for the advice. $\endgroup$– langFeb 18, 2014 at 6:52
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4$\begingroup$ Is this trivial? I don't think so. $\endgroup$– Brendan McKayFeb 18, 2014 at 7:02
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3$\begingroup$ I think it not easy. There are also many papers to find the genus of this kind of graph. For example this one sciencedirect.com/science/article/pii/0095895675900830 $\endgroup$– langFeb 18, 2014 at 7:27
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2$\begingroup$ One lower bound is the genus of $K_{m,4,2}$ which is $m-2$, according to sciencedirect.com/science/article/pii/S0195669804000617 $\endgroup$– Douglas ZareMar 27, 2014 at 9:05
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