D'aniel Varga

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6 papers · 1 filter

math.CO2026

A unit-distance graph in the plane with independence ratio below 1/4

Ãkos DÃºcz, DÃ¡niel 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…

math.CO2026

Improved bounds for the double cap conjecture

Domonkos Czifra, Ãkos DÃºcz, MÃ¡tÃ© Matolcsi +2

In 1974, Witsenhausen asked for the maximum possible density $I^\pm_{n}$ of a measurable subset $A$ of the unit sphere $S^{n - 1} \subset R^{n}$ such that $A$ contains no p…

math.CO2025

Triplets of Mutually Unbiased Bases

MÃ¡te Matolcsi, Ãkos K. Matszangosz, DÃ¡niel Varga +1

We initiate a systematic study of triplets of mutually unbiased bases (MUBs). We show that in $C^{d}$ each MUB-triplet is characterized by a $d \times d \times d$ object that…

math.CO2025

Diverse beam search to find densest-known planar unit distance graphs

Peter Engel, Owen Hammond-Lee, Yiheng Su +2

This paper addresses the problem of determining the maximum number of edges in a unit distance graph (UDG) of $n$ vertices using computer search. An unsolved problem of Paul ErdÅs…

math.CO2025

The fractional chromatic number of the plane is at least 4

We prove that the fractional chromatic number $I ¨ _{f} (R^{2})$ of the unit distance graph of the Euclidean plane is greater than or equal to $4$ . Interestingly, however, we cann…

math.CO2025

Piercing intersecting convex sets

Imre BÃ¡rÃ¡ny, Travis Dillon, DÃ¶mÃ¶tÃ¶r PÃ¡lvÃ¶lgyi +1

Assume two finite families $A$ and $B$ of convex sets in $R^{3}$ have the property that $A \cap B \neq = \emptyset$ for every $A \in A$ and $B\in \math…