## New answers tagged spectral-graph-theory

2
votes

### Existence of disjoint expanders in a graph

One can even partition the edges of $K_n$ into bounded-degree expanders. Let $\epsilon > 0$ be small and $n$ be sufficiently large. Let $H$ be an $n$-vertex edge-expander with $\Delta(H) \leq 3$. ...

5
votes

### Existence of disjoint expanders in a graph

Yes, and you can find many more than $\log n$ of them.
Take an expander $G$ (for example a random cubic graph).
Take $k$ copies, where $k=o(n^{1/2})$. Now randomly
relabel each copy. The probability ...

4
votes

### Is there a version of Weyl's law for graph Laplacians?

There will certainly exist a Weyl law for random planar graphs. However, the nature of the law will depend very sensitively on exactly which model of random graphs one takes.
One can start to see this ...

1
vote

### Is there a version of Weyl's law for graph Laplacians?

For $N_\lambda$ denoting the number of eigenvalues less than $\lambda$, Weyl's law gives the asymptotics of $N_\lambda$ as $\lambda$ tends to infinity. The usual approach to establish this asymptotics ...

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