Work

Ramsey numbers of cycles in random graphs

Year: 2024

Type: article

Abstract: Let be the Ramsey number of the cycle on vertices. We prove that, for some , with high probability every 2‐coloring of the edges of has a monochromatic copy of , as long as and . This is sharp up to the value of and it improves results of Letzter and of Krivelevich, Kronenberg, and Mond.

Source: Random Structures and Algorithms

DOI: 10.1002/rsa.21253

Authors: Pedro Araújo, Matías Pavez‐Signé, Nicolás Sanhueza‐Matamala

Institutions: Czech Technical University in Prague, Centre National de la Recherche Scientifique, Center for Mathematical Modeling, University of Chile, University of Concepción

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Grantová Agentura České Republiky, H2020 European Research Council

Awards: Random discrete structures, Spanning Subgraphs in Graphs