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math.CO2021
A New Upper Bound for the Ramsey Number of Fans
Vojtěch Dvořák, Harry Metrebian
A fan is a graph consisting of triangles, all having precisely one common vertex. Currently, the best known bounds for the Ramsey number are $9n/2-5 \leq R(F_n)…
math.CO2021
The Maker-Breaker percolation game on the square lattice
Vojtěch Dvořák, Adva Mond, Victor Souza
We study the Maker-Breaker percolation game on , introduced by Day and Falgas-Ravry. As our first result, we show that Breaker has a winning strategy for the…