Dan Hefetz

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math.CO2026

On graphs whose cycle space is spanned by their Hamilton cycles

Dan Hefetz, Michael Krivelevich

The cycle space of a graph $G$ , denoted $C (G)$ , is a vector space over $F_{2}$ , spanned by all incidence vectors of edge-sets of cycles of $G$ . If $G$ has $n$ ver…

math.CO2025

The Hamilton cycle space of random regular graphs and randomly perturbed graphs

Dan Hefetz, Michael Krivelevich

The cycle space of a graph $G$ , denoted $C (G)$ , is a vector space over $F_{2}$ , spanned by all incidence vectors of edge-sets of cycles of $G$ . If $G$ has $n$ vertices, the…

math.CO2025

The Hamilton cycle space of random graphs

Dan Hefetz, Michael Krivelevich

The cycle space of a graph $G$ , denoted $C (G)$ , is a vector space over $F_{2}$ , spanned by all incidence vectors of edge-sets of cycles of $G$ . If $G$ has $n$ vertices, the…

math.CO2025

Ramsey properties of randomly perturbed hypergraphs

Elad Aigner-Horev, Dan Hefetz, Mathias Schacht

We study Ramsey properties of randomly perturbed $3$ -uniform hypergraphs. For~ $t \geq 2$ , write $K ~_{t}^{(3)}$ to denote the $3$ -uniform {\it expanded} clique hypergraph obtaine…

math.CO2024

Smoothed Analysis of the KomlÃ³s Conjecture: Rademacher Noise

Elad Aigner-Horev, Dan Hefetz, Michael Trushkin

The {\em discrepancy} of a matrix $M \in R^{d \times n}$ is given by $DISC (M) := min_{x \in {- 1, 1}^{n}} ∥ M x ∥_{\infty}$ . An outstanding…