4 papers
On the maximal measure of a spherical set avoiding solutions to x + y + z = 0
Ákos 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
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…
A note on geometric colorings of the Moser lattice
Ákos 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…
Domination and packing in graphs
Ákos 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 maximum…