3 papers
math.CO2026
On Balance, To What Degree is Burr's Conjecture True?
Shagnik Das, Bruce Reed, Jozef Skokan
For many trees , the Ramsey number of , denoted by , is determined by the sizes of the partition classes in its unique bipartition. In 1976, Burr proved that…
math.CO2026
A degree version of the Burr-ErdÅs conjecture on trees
Jasmin Katz, MatÃas Pavez-Signé, Jozef Skokan
An old conjecture of Burr and Erd\H os states that the Ramsey number of any -vertex tree is at most . In 2012, Schelp asked whether a degree version of the Burr--ErdÅ…
math.CO2025
Alternating paths in oriented graphs with large semidegree
Jozef Skokan, Mykhaylo Tyomkyn
In new progress on conjectures of Stein, and Addario-Berry, Havet, Linhares Sales, Reed and Thomassé, we prove that every oriented graph with all in- and out-degrees greater than…