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math.CO2026
A unit-distance graph in the plane with independence ratio below 1/4
Ákos Dúcz, Dániel Varga
We prove that there exists a finite unit-distance graph in the plane with independence ratio strictly smaller than 1/4, answering a question of Erdős. Our proof closely follows the…
math.CO2026
Improved bounds for the double cap conjecture
Domonkos Czifra, Ákos Dúcz, Máté Matolcsi +2
In 1974, Witsenhausen asked for the maximum possible density of a measurable subset of the unit sphere such that contains no pa…