Rafael Miyazaki

collaborators

4 papers

math.CO2026

Ramsey properties for tilings in random graphs

Lucas AragÃ£o, Xinbu Cheng, Rafael Filipe +3

Let $m H$ be the graph formed by $m$ vertex-disjoint copies of a graph $H$ . Let $G \to (H)_{r}$ denote that, in any $r$ -colouring of the edges of $G$ , there exists a monochromatic cop…

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

A note on the maximum ratio between chromatic number and clique number

Igor Araujo, Rafael Filipe, Rafael Miyazaki

Let $f (n)$ be the maximum, over all graphs $G$ on $n$ vertices, of the ratio $\frac{I ¨ ( G )}{I ¨ ( G )}$ , where $I ¨ (G)$ denotes the chromatic number of $G$ and $I ¨ (G)$ the clique number…

math.CO2025

Chromatic Polynomial Evaluation Spectra

Rafael Miyazaki, Cosmin Pohoata, Michael Zheng

Around 10 years ago, Agol and Krushkal showed that the number of chromatic polynomials $P_{G}$ arising from graphs $G$ on $n$ vertices grows exponentially with $n$ , by establishing…