E. Mulrenin

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20242026

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3 papers · 2 filters

math.CO2026

Recursive upper bounds for the vertex online Ramsey game with applications to hypergraph Ramsey numbers

Dániel Dobák, Eion Mulrenin

The classical recursive upper bound on hypergraph Ramsey numbers due to Erdős and Rado states that for $2 \leq k < s \leq t$ , \[ r_k(s,t) \leq 2^{\binom{r_{k-1}(s-1,t-1)}{k-1}}. \]…

math.CO2026

Improved Ramsey bounds for generalized Schur equations

Rafael Miyazaki, Eion Mulrenin, Cosmin Pohoata +1

We show that for $m, r \in N$ and $N > (2 m + 1)^{r} (r!)^{1/ m}$ , every $r$ -coloring of the integers in the interval $[N]$ contains a monochromatic solution to the equation \[…

math.CO2026

Two counterexamples to a conjecture about even cycles

David Conlon, Eion Mulrenin, Cosmin Pohoata

A conjecture of Verstraëte states that for any fixed $ℓ < k$ there exists a positive constant $c$ such that any $C_{2 k}$ -free graph $G$ contains a $C_{2 ℓ}$ -free subgraph with…