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I am interested in graph Ramsey theory. Are there any papers which investigate Ramsey numbers $R(G,G)$ of an arbitrary graph by analyzing the spectrum of $G$? In general, has anyone found any connection between graph spectra and ramsey numbers? I tried to search for literature on the internet but nothing turned up.


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Actually, I think you are right and there are not such papers that exactly match with your subject. But, some probabilistic techniques used spectral theory to find some bounds for Ramsey number. One of this paper is famous:

"Asymptotically tight bounds for some multicolored Ramsey numbers" by "Noga Alon" and "Vojtech Rodl"

So, if you change your keywords for searching based on this paper and its references, you might be more successful.

Also, the below paper is good:

"Extremal and Probabilistic Combinatorics" by "N. Alon" and "M. Krivelevich".

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