Timeline for Genus of the graph $K_{4,2,2,2}$
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Apr 15, 2018 at 14:53 | vote | accept | bor | ||
| Jan 28, 2018 at 17:51 | answer | added | Timothy Sun | timeline score: 14 | |
| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Mar 28, 2014 at 7:15 | comment | added | bor | @j.c. I think the proof of Theorem 4.1 is not correct and the result is not correct. | |
| Mar 27, 2014 at 13:52 | comment | added | bor | Thank you so much @j.c. . I will also try to understand the paper.. | |
| Mar 27, 2014 at 13:40 | comment | added | j.c. | @bor I find their proof of Theorem 4.1 very unclear. Here is a copy of their paper dl.dropboxusercontent.com/u/8101832/bettayebnguyen.pdf . And by the way, the paper cited by Felix Goldberg has a longer preprint version here preprint.math.uni-hamburg.de/public/papers/hbm/hbm2006251.pdf , the published article in particular refers to this version for more background | |
| Mar 27, 2014 at 13:02 | comment | added | bor | @j.c. That a serious problem. Actually I don't have any access to this paper. Can you Figure what is the problem? | |
| Mar 27, 2014 at 11:24 | comment | added | j.c. | If I'm not misreading, Theorem 4.1 from the reference given by David Wood states that the genus of the complete k-partite graph with partitions of sizes $V_1,V_2,\dots,V_k$ is $\sum_{i<j}\left\lceil\frac{(V_i-2)(V_j-2)}{4}\right\rceil+\left\lceil\frac{(k-3)(k-4)}{12}\right\rceil$, which gives zero for your graph. It also gives 1 for $K_{4,4,2}$ so I'm not sure what's going on. | |
| Mar 27, 2014 at 10:37 | comment | added | David Wood | Here is a paper that seems relevant (based on the title): Said Bettayeb, Quan T. Nguyen, "The genus of the complete multipartite graph and the complete multi-layered graph," aiccsa, pp.1-4, ACS/IEEE International Conference on Computer Systems and Applications - AICCSA 2010, 2010. doi.ieeecomputersociety.org/10.1109/AICCSA.2010.5587024 | |
| Mar 27, 2014 at 10:14 | comment | added | Felix Goldberg | Since the answer is between $2$ and $4$, as shown by @DouglasZare, you might want to try the algebraic approach of Diestel and Bruhn (sciencedirect.com/science/article/pii/S0095895608000476). In fact, you might want to contact Henning Bruhn who might be able to compute this for you using their characterization! | |
| Mar 27, 2014 at 9:14 | comment | added | Douglas Zare | One lower bound is the genus of $K_{4,4,2}$, which is $2$. An upper bound is the genus of $K_{10}$, which is $4$. | |
| Mar 27, 2014 at 8:34 | comment | added | bor | @F.C. But that question has no answer. If that question has an answer, then it will be an answer to this question also. | |
| Mar 27, 2014 at 8:14 | comment | added | F. C. | See question mathoverflow.net/questions/157894/genus-of-the-graph-k-m-2-2-2 | |
| Mar 27, 2014 at 7:11 | comment | added | bor | I have added... | |
| Mar 27, 2014 at 7:10 | history | edited | bor | CC BY-SA 3.0 |
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| Mar 27, 2014 at 6:25 | comment | added | Tim Porter | You could, perhaps, add a brief definition of this graph. | |
| Mar 27, 2014 at 5:32 | history | edited | bor | CC BY-SA 3.0 |
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| Mar 27, 2014 at 4:48 | history | asked | bor | CC BY-SA 3.0 |