Graphes expanseurs et crible dans les structures combinatoires
Idioma
en
Article de revue
Este ítem está publicado en
Journal of the Australian Mathematical Society. 2018, vol. 105, n° 1, p. 79--102
Cambridge University Press
Resumen en inglés
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 ...Leer más >
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.< Leer menos
Palabras clave en inglés
Groups
Random Walks
Graphs
Sieve
Orígen
Importado de HalCentros de investigación