E. Mulrenin

collaborators

6 papers

math.CO2026

Some remarks on Folkman graphs for triangles

Eion Mulrenin, Steven Van Overberghe

Folkman's theorem asserts the existence of graphs $G$ which are $K_{4}$ -free, but which have the property that every two-coloring of $E (G)$ contains a monochromatic triangle. The qua…

math.CO2026

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

DÃ¡niel DobÃ¡k, Eion Mulrenin

The classical recursive upper bound on hypergraph Ramsey numbers due to ErdÅs 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 VerstraÃ«te 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 wit…

math.CO2025

Color avoidance for monotone paths

Eion Mulrenin, Cosmin Pohoata, Dmitrii Zakharov

In 2014, Moshkovitz and Shapira determined the tower height for hypergraph Ramsey numbers of tight monotone paths. We address the color-avoiding version of this problem in which on…

math.CO2025

Even cycles in graphs avoiding longer even cycles

David Conlon, Eion Mulrenin, Cosmin Pohoata

A conjecture of VerstraÃ«te 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 wit…