Ramsey numbers of cycles in random graphs
Pedro Ara\'ujo, Mat\'ias Pavez-Sign\'e, and Nicol\'as, Sanhueza-Matamala

TL;DR
This paper establishes sharp probabilistic bounds for the Ramsey numbers of cycles in random graphs, showing that with high probability, certain edge colorings contain monochromatic cycles under specified conditions.
Contribution
It improves existing bounds on Ramsey numbers of cycles in random graphs, providing sharper probabilistic thresholds and extending previous results.
Findings
High probability existence of monochromatic cycles in random graphs
Sharp bounds on the Ramsey number thresholds for cycles
Improved results over previous work by Letzter and Krivelevich et al.
Abstract
Let be the Ramsey number of the cycle on vertices. We prove that, for some , with high probability every -colouring 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.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory
