Noga Alon

activity

20242026

collaborators

10 papers

math.CO2026

Pseudoshattering Pairs

Noga Alon, Varun Sivashankar

For two vectors $x, y \in [b]^{k}$ , consider the bipartite graph with two copies of $[b]$ in which $i$ on the left is joined to $j$ on the right if $(x_{t}, y_{t}) = (i, j)$ for some coordinat…

math.CO2026

Packing arithmetic progressions

Noga Alon, MichaÅ DÄbski, JarosÅaw Grytczuk +1

Let $F = {A_{1}, A_{2}, \dots, A_{k}}$ be a collection of finite arithmetic progressions, where each $A_{d}$ is an initial segment of the set $D_{d} = {d, 2 d, 3 d, \dots}$ of consecutiv…

math.CO2025

Distinct Directions and Distinct Distances in $R^{d}$

Noga Alon, Rom Pinchasi

We show that there exists an absolute positive constant $b (\geq \frac{1}{48})$ so that any set of $n$ points in $R^{d}$ that is $d$ -dimensional determines at least $b d n$ li…

math.CO2025

The spanning tree spectrum: improved bounds and simple proofs

Noga Alon, Matija BuciÄ, Lior Gishboliner

The number of spanning trees of a graph $G$ , denoted $I ¨ (G)$ , is a well studied graph parameter with numerous connections to other areas of mathematics. In a recent remarkable pape…

math.CO2025

Sums along the edges of bounded degree graphs

Noga Alon, Itai Benjamini, Georgii Zakharov +1

Let $G$ be a graph on $n$ vertices and $(H, +)$ be an abelian group. What is the minimum size $S_{H} (G)$ of the set of all sums $A (u) + A (v)$ over all injections $A : V (G) \to H$ ? In…

math.CO2025

Essentially tight bounds for rainbow cycles in proper edge-colourings

Noga Alon, Matija BuciÄ, Lisa Sauermann +2

An edge-coloured graph is said to be rainbow if no colour appears more than once. Extremal problems involving rainbow objects have been a focus of much research over the last decad…

Pseudoshattering Pairs

Packing arithmetic progressions

Distinct Directions and Distinct Distances in Rd

The spanning tree spectrum: improved bounds and simple proofs

Sums along the edges of bounded degree graphs

Essentially tight bounds for rainbow cycles in proper edge-colourings

Distinct Directions and Distinct Distances in $R^{d}$