Florian Pfender

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math.CO2026

A short proof that $R (3, k) = Θ (k^{2} / lo g k)$

Samuel Harris, Zion Hefty, Paul Horn +2

We give a nibble-free construction proving $R (3, k) \geq (1/200 + o (1)) k^{2} / lo g k$ . We also include Shearer's proof bounding the independence number of a triangle-free graph, which impli…

math.CO2025

A polynomial improvement for the odd cycle-complete Ramsey numbers

Marcelo Campos, Matthew Jenssen, Marcus Michelen +2

We give a polynomial improvement to the cycle-complete Ramsey numbers \[ r(C_{\ell},K_k) \geq k^{1+1/(\ell- 2) + \varepsilon_{\ell} + o(1)}, \] for all fixed odd $ℓ > 7$ with $k…

math.CO2025

Improving $R (3, k)$ in just two bites

Zion Hefty, Paul Horn, Dylan King +1

We present a flexible random construction which, for certain graphs $H$ , is able to produce $H$ -free graphs with edge density strictly larger than that of the $H$ -free process, whi…

A short proof that R(3,k)=Θ(k2/logk)

A polynomial improvement for the odd cycle-complete Ramsey numbers

Improving R(3,k) in just two bites

A short proof that $R (3, k) = Θ (k^{2} / lo g k)$

Improving $R (3, k)$ in just two bites