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3 questions
2
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Expansion of random subgraphs of a bi-regular bipartite graph
Let $G = (L, R, E)$ be a bi-regular bipartite graph, with $|L|=n$ and $|R| = C \cdot n$, where $C$ is a large constant. Let $d$ be its (constant) right-degree.
We know $G$ is a good spectral expander. ...
0
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0
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4-cycles vs eigenvalue information on quasi-random graphs
My (philosophical) question arises from reading the wonderful paper of Chung-Graham-Wilson where the authors introduces the notion of quasi-random graphs.
The main purpose of the paper is to show ...
8
votes
2
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Spectrum of the Laplacian on G(n, p) and G(n, M)
A random graph in $G(n, p)$ model is a graph on $n$ vertices in which for each of the $n\choose{2}$ edges we independently flip a coin, then take the edge with probability $p$ or remove it with $1 - p$...