5 papers
On the maximal measure of a spherical set avoiding solutions to x + y + z = 0
Ãkos Dúcz
We prove that the maximal normalized surface measure of a spherical set in d dimensions avoiding solutions to x + y + z = 0 approaches 1/2 as d goes to infinity. This gives a parti…
A unit-distance graph in the plane with independence ratio below 1/4
Ãkos 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 ErdÅs. Our proof closely follows th…
A note on geometric colorings of the Moser lattice
Ãkos Dúcz
In arXiv:2311.10069, Matolcsi et al. show that the fractional chromatic number of the plane is at least 4. Their proof uses a 27-vertex unit-distance graph in the Moser lattice, wi…
Improved bounds for the double cap conjecture
Domonkos Czifra, Ãkos 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 p…
Domination and packing in graphs
Ãkos Dúcz, Anna Gujgiczer
The dominating number of a graph is the minimum size of a vertex set whose closed neighborhoods cover all vertices of , while the packing number is the maxim…