Author

Pedram Noohi

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Preprint Oct 2026

Decay-Ramsey Sequences

Given a sequence $\mathbf{a}=(a_i)_{i\geq 1}$ of positive real numbers, we say that a colouring $c:E(K_n)\to \mathbb{N}$ is $\mathbf{a}$-bounded if the proportion of edges coloured $i$ is at most $a_i$, for all $i$. We write \[ \mathbf{a}\, \to\, K_k \] if, for all sufficiently large $n$, all $\mathbf{a}$-bounded colou...

Francesco Di Braccio, Simon Griffiths, Pedram Noohi et al. · 0 citations

Preprint Oct 2026

Hypergraphs with the smallest Hall ratio are still hard to colour

For $H$ a hypergraph, the Hall ratio $\rho(H)=\text{max}_{X\subseteq V(H)}\frac{\lvert{X}\rvert}{\alpha(H[X])}$ is a natural lower bound for its chromatic number, and among non-empty $k$-uniform hypergraphs the smallest possible Hall ratio is $k/(k-1)$. For graphs ($k = 2$), having minimum Hall ratio $2$ forces chromat...

Veronica Bitonti, Freddie Illingworth, Pedram Noohi et al. · 0 citations