Eric Li

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math.CO2026

The Godsil--McKay Asymptotic for Latin Rectangles in the Sublinear Range of Erdős Problem 725

Eric Li

Erdős Problem 725 asks for an asymptotic formula for the number $L_{k, n}$ of ordered, labelled $k \times n$ Latin rectangles. Godsil and McKay proved that $L_{k,n}\sim (n!)^k((n)_k/…

math.CO2026

A Resolution of Erdős Problem 550 on Tree versus Complete Multipartite Ramsey Numbers

Eric Li

We resolve Erdős Problem 550, originally asked as question (2) of Erdős, Faudree, Rousseau, and Schelp. Precisely, for fixed integers $k \geq 2$ and $1 \leq m_{1} \leq \dots \leq m_{k}$ ,…

math.CO2026

A Resolution of Erdős Problems 593 and 1177: Obligatory Triple Systems and Exact Spectra

Eric Li

We resolve Erdős Problems #593 and #1177. Problem #593 asks which finite triple systems occur in every uncountably chromatic triple system; the answer is exactly the class generate…

math.CO2026

The Erdős-Hajnal High-Girth Subgraph Conjecture Holds in the Polynomial Chromatic-Sparsity Regime

Eric Li

For a graph $G$ put $h_{r} (G) = max χ (H) : H \subseteq G, girth (H) \geq r .$ Erdős and Hajnal asked whether $h_{r} (G) \to \infty$ as $χ (G) \to \infty$ , for every fixed $r \geq 4$ . We…

math.CO2026

On the Duke--Erdős--Rödl Problem at the One-Third Threshold

Eric Li

Let $G$ be an $n$ -vertex graph with $e (G) \geq n^{2} / k$ . We prove a self-contained internal short-cycle core theorem at the threshold $k \leq n^{1/3}$ : the graph $G$ contains a subgraph…