Work

The asymptotic of off-diagonal online Ramsey numbers for paths

Year: 2024

Type: article

Abstract: We prove that for every k≥10, the online Ramsey number for paths Pk and Pn satisfies r̃(Pk,Pn)≥53n+k9−4, matching up to a linear term in k the upper bound recently obtained by Bednarska-Bzdęga (2024). In particular, this implies limn→∞r̃(Pk,Pn)n=53, whenever 10≤k=o(n), disproving a conjecture by Cyman et al. (2015).

Source: European Journal of Combinatorics

DOI: 10.1016/j.ejc.2024.104032

Authors: Adva Mond, Julien Portier

Institution: University of Cambridge

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,000

Funders: Cambridge Trust, Engineering and Physical Sciences Research Council, Trinity College, University of Cambridge