Expander graphs and sieving in combinatorial structures

Abstract : We prove a general large sieve statement in the context of random walks on subgraphs of a given graph. This can be seen as a generalization of previously known results where one performs a random walk on a group enjoying a strong spectral gap property. In such a context the point is to exhibit a strong uniform expansion property for a suitable family of Cayley graphs on quotients. In our combinatorial approach, this is replaced by a result of Alon--Roichman about expanding properties of random Cayley graphs. Applying the general setting we show e.g., that with high probability (in a strong explicit sense) random coloured subsets of integers contain monochromatic (non-empty) subsets summing to zero, or that a random coloring of the edges of a complete graph contains a monochromatic triangle.
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https://hal.archives-ouvertes.fr/hal-00693334
Contributor : Jean-Sébastien Sereni <>
Submitted on : Friday, January 6, 2017 - 12:08:59 PM
Last modification on : Tuesday, December 18, 2018 - 4:38:02 PM
Long-term archiving on : Friday, April 7, 2017 - 1:25:12 PM

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  • HAL Id : hal-00693334, version 3
  • ARXIV : 1205.0631

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Florent Jouve, Jean-Sébastien Sereni. Expander graphs and sieving in combinatorial structures. 2017. ⟨hal-00693334v3⟩

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