Tag Archives: pseudorandom graphs

Kopparty’s graph

Alon’s construction of optimal pseudorandom graphs from 1994 is useful for obtaining several interesting combinatorial results in various areas of mathematics, some of which are highlighted in this survey of Noga from last year (also see my previous post). In … Continue reading

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Ramsey numbers from pseudorandom graphs

One of the foundational results in modern combinatorics is Ramsey’s theorem which states that for every positive integers there exists a constant such that for all , every -coloring of edges of the complete graph has a monochromatic copy of … Continue reading

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Pseudorandom clique-free graphs

Pseudorandom graphs are graphs that in some way behaves like a random graph with the same edge density. One way in which this happens is as follows. In the random graph , with , a direct application of Chernoff bound … Continue reading

Posted in Combinatorics, Extremal Combinatorics, Spectral Graph Theory | Tagged , , | 5 Comments