Patrick Morris

collaborators

7 papers

math.CO2026

Counting subsets of integers free of arithmetic configurations

Patrick Morris, Miquel Ortega, Juanjo RuÃ©

Cameron and ErdÅs asked if the number of sets free of arithmetic progressions of length $k$ is $2^{r_{k} (n) (1 + o (1))}$ , where $r_{k} (n)$ is the maximum cardinality of a $k$ -AP-free sub…

math.CO2026

Universality for transversal Hamilton cycles

Candida Bowtell, Patrick Morris, Yanitsa Pehova +1

Let $G = {G_{1}, \dots, G_{m}}$ be a graph collection on a common vertex set $V$ of size $n$ such that $I^´ (G_{i}) \geq (1 + o (1)) n /2$ for every $i \in [m]$ . We show that $\mathbf…

math.CO2026

A canonical Ramsey theorem for even cycles in random graphs

JosÃ© D. Alvarado, Y. Kohayakawa, Patrick Morris +1

The celebrated canonical Ramsey theorem of ErdÅs and Rado implies that for $2 \leq k \in N$ , any colouring of the edges of $K_{n}$ with $n$ sufficiently large gives a copy of…

math.CO2026

A sparse canonical van der Waerden theorem

JosÃ© D. Alvarado, Yoshiharu Kohayakawa, Patrick Morris +2

The canonical van der Waerden theorem asserts that, for sufficiently large $n$ , every colouring of $[n]$ contains either a monochromatic or a rainbow arithmetic progression of leng…

math.CO2026

A canonical Ramsey theorem with list constraints in random (hyper-)graphs

The celebrated canonical Ramsey theorem of ErdÅs and Rado implies that for a given $k$ -uniform hypergraph (or $k$ -graph) $H$ , if $n$ is sufficiently large then any colouring of th…

math.CO2026

A note on multicolour Ramsey numbers and random sphere graphs

Yamaan Attwa, Albert LÃ³pez Vidal, Patrick Morris

The Ramsey number $r (t; ℓ)$ is the smallest $n$ such that every $ℓ$ -coloring of the edges of $K_{n}$ gives a monochromatic $K_{t}$ . In recent years, there have been several impr…