A canonical Ramsey theorem with list constraints in random graphs

Autor(es)

Alvarado, Jose D. ; Kohayakawa, Yoshiharu ; Morris, Patrick ; Mota, Guilherme Oliveira

• Tipo de documento: Artigo Científico
• Fonte: XII LATIN-AMERICAN ALGORITHMS, GRAPHS AND OPTIMIZATION SYMPOSIUM, LAGOS 2023; v. 224, p. 7-pg., 2023-01-01.

Resumo

The celebrated canonical Ramsey theorem of Erclos and Rado implies that for a given graph H, if n is sufficiently large then any colouring of the edges of K-n gives rise to copies of H that exhibit certain colour patterns, namely monochromatic, rainbow or lexicographic. We are interested in sparse random versions of this result and the threshold at which the random graph G(n, p) inherits the canonical Ramsey properties of K-n. Our main result here pins down this threshold when we focus on colourings that are constrained by some prefixed lists. This result is applied in an accompanying work of the authors on the threshold for the canonical Ramsey property (with no list constraints) in the case that H is an even cycle. (C) 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (httpslicreativecommons.orgilicenses/bv-nc-nd/4.0) (AU)

• Processo FAPESP: 18/04876-1 - Teoria de Ramsey, teoria estrutural de grafos e aplicações em Bioinformática
• Beneficiário: Guilherme Oliveira Mota
• Modalidade de apoio: Auxílio à Pesquisa - Jovens Pesquisadores
• Processo FAPESP: 19/13364-7 - Problemas extremais e estruturais em teoria dos grafos
• Beneficiário: Cristina Gomes Fernandes
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 20/10796-0 - Problemas estruturais em grafos aleatórios
• Beneficiário: José Diego Alvarado Morales
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado