A canonical Ramsey theorem with list constraints in random graphs

Author(s)

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

• Document type: Journal article
• Source: XII LATIN-AMERICAN ALGORITHMS, GRAPHS AND OPTIMIZATION SYMPOSIUM, LAGOS 2023; v. 224, p. 7-pg., 2023-01-01.

Abstract

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)

• FAPESP's process: 18/04876-1 - Ramsey theory, structural graph theory and applications in Bioinformatics
• Grantee: Guilherme Oliveira Mota
• Support Opportunities: Research Grants - Young Investigators Grants
• FAPESP's process: 19/13364-7 - Extremal and structural problems in graph theory
• Grantee: Cristina Gomes Fernandes
• Support Opportunities: Regular Research Grants
• FAPESP's process: 20/10796-0 - Structural problems in random graphs
• Grantee: José Diego Alvarado Morales
• Support Opportunities: Scholarships in Brazil - Post-Doctoral