Timeline for Cheeger Numbers for 3-regular Graphs
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 18, 2015 at 8:54 | history | edited | Gordon Royle | CC BY-SA 3.0 |
Added more data to the answer
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| Jun 16, 2015 at 14:20 | comment | added | user71114 | I have one happy student now. Another aspect of Pappus being special is that for n=16 the max is smaller than for n=18, and for n=20 it stays the same (if I can now trust his program); whereas in general the max seems to decrease (or stay the same) as n increases. Of course these small values don't mean much. | |
| Jun 16, 2015 at 14:11 | vote | accept | CommunityBot | ||
| Jun 16, 2015 at 12:19 | comment | added | Sebi Cioaba | Nozaki studied a similar problem (among all k-regular graphs of given order v, find the one(s) with the smallest second eigenvalue of the adjacency matrix): arxiv.org/abs/1407.4562 Nozaki obtained a linear programming bound for graphs. With Nozaki, Koolen and Vermette, I studied a related, but different problem (given $k$ and $\lambda$, find the largest order of a $k$-regular graph with second eigenvalue at most $\lambda$); we used Nozaki's LP bound and interlacing. The Pappus graph appeared as extremal (largest cubic graph with $\lambda_2\leq \sqrt{3}$): arxiv.org/abs/1503.06286 | |
| Jun 16, 2015 at 8:45 | history | answered | Gordon Royle | CC BY-SA 3.0 |