Rafael Miyazaki

collaborators

5 papers

math.CO2026

A base- $8$ upper bound for planar peeling sequences

André Hisatsuga, Griffin Johnston, Rafael Miyazaki

Let $g (n)$ denote the minimum number of peeling sequences among all $n$ -point sets in general position in the plane. Dumitrescu and Tóth proved an exponential upper bound with base…

math.CO2026

Ramsey properties for tilings in random graphs

Lucas Aragão, 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.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…

math.CO2025

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 $\frac{χ ( G )}{ω ( G )}$ , where $χ (G)$ denotes the chromatic number of $G$ and $ω (G)$ the clique number of $…

A base-8 upper bound for planar peeling sequences

Ramsey properties for tilings in random graphs

Improved Ramsey bounds for generalized Schur equations

Chromatic Polynomial Evaluation Spectra

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

A base- $8$ upper bound for planar peeling sequences