Timeline for The middle eigenvalues of an undirected graph
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
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| Mar 15, 2010 at 22:08 | comment | added | Kevin P. Costello | The point is that any actual solution has $\sum \lambda_i^4$ at least as large as the hypothetical (perhaps noninteger) solution I wrote down. To put it differently, what I'm doing is taking the inequality $(x t^2+(1-x)9^2 \geq (xt+(1-x)9)^2$, then for each $i$ choosing an appropriate $x$ so that the right hand side is $(\lambda_i^2)^2$. Adding up over all $i$ then gives the same bound. | |
| Mar 15, 2010 at 20:18 | comment | added | alex | Why is it true that every $\lambda_i^2$ is either $t$ or $9$? It seems like its possible that $\sum_i \lambda_i^2 = 3n$ has no solution at all if we require each $\lambda_i^2 \in \{ t, 9\}$. | |
| Mar 15, 2010 at 17:28 | history | answered | Kevin P. Costello | CC BY-SA 2.5 |