Matías Pavez-Signé

activity

20202026

most citedRamsey numbers of bounded degree trees versus general graphs

6 citations · 10 across the 11 of their papers we have counts for

collaborators

12 papers

math.CO2026

A degree version of the Burr-Erdős conjecture on trees

Jasmin Katz, Matías Pavez-Signé, Jozef Skokan

An old conjecture of Burr and Erd\H os states that the Ramsey number of any $n$ -vertex tree $T$ is at most $2 n - 2$ . In 2012, Schelp asked whether a degree version of the Burr--Erdős…

math.CO2024

Monochromatic partitions in 2-edge-coloured bipartite graphs

Camila Fernández, Matías Pavez-Signé, Maya Stein

We study two variations of the Gyarfas--Lehel conjecture on the minimum number of monochromatic components needed to cover an edge-coloured complete bipartite graph. Specifically,…

math.CO2023

Spanning trees in pseudorandom graphs via sorting networks

Joseph Hyde, Natasha Morrison, Alp Müyesser +1

We show that $(n, d, λ)$ -graphs with $λ = O (d / lo g^{3} n)$ are universal with respect to all bounded degree spanning trees. This significantly improves upon the previous best bound due t…

math.CO2023★ 6 cited

Ramsey numbers of bounded degree trees versus general graphs

Richard Montgomery, Matías Pavez-Signé, Jun Yan

For every $k \geq 2$ and $Δ$ , we prove that there exists a constant $C_{Δ, k}$ such that the following holds. For every graph $H$ with $χ (H) = k$ and every tree with at least $C_{Δ,k}|H…

math.CO2023★ 2 cited

Counting spanning subgraphs in dense hypergraphs

Richard Montgomery, Matías Pavez-Signé

We give a simple method to estimate the number of distinct copies of some classes of spanning subgraphs in hypergraphs with high minimum degree. In particular, for each $k \geq 2$ a…

math.CO2023

Spanning trees in the square of pseudorandom graphs

Matías Pavez-Signé

We show that for every $Δ \in N$ , there exists a constant $C$ such that if $G$ is an $(n, d, λ)$ -graph with $d / λ \geq C$ and $d$ is large enough, then $G^{2}$ contains every $n$ -ve…

math.CO2023

Spanning subdivisions in Dirac graphs

Matías Pavez-Signé

We show that for every $n \in N$ and $lo g n \leq d \leq n$ , if a graph $G$ has $N = Θ (d n)$ vertices and minimum degree $(1 + o (1)) \frac{N}{2}$ , then it contains a spanning subdivisi…

math.CO2022★ 1 cited

Ramsey numbers with prescribed rate of growth

Matías Pavez-Signé, Simón Piga, Nicolás Sanhueza-Matamala

Let $R (G)$ be the two-colour Ramsey number of a graph $G$ . In this note, we prove that for any non-decreasing function $n \leq f (n) \leq R (K_{n})$ , there exists a sequence of connect…

math.CO2022

Ramsey numbers of cycles in random graphs

Pedro Araújo, Matías Pavez-Signé, Nicolás Sanhueza-Matamala

Let $R (C_{n})$ be the Ramsey number of the cycle on $n$ vertices. We prove that, for some $C > 0$ , with high probability every $2$ -colouring of the edges of $G (N, p)$ has a monochroma…

math.CO2021★ 1 cited

Towards a hypergraph version of the Pósa-Seymour conjecture

Matías Pavez-Signé, Nicolás Sanhueza-Matamala, Maya Stein

We prove that for fixed $r \geq k \geq 2$ , every $k$ -uniform hypergraph on $n$ vertices having minimum codegree at least $(1 - ((k - 1 r - 1) + (k - 2 r - 2))^{- 1}) n + o (n)$ contains t…

math.CO2020

Dirac-type conditions for spanning bounded-degree hypertrees

Matías Pavez-Signé, Nicolás Sanhueza-Matamala, Maya Stein

We prove that for fixed $k$ , every $k$ -uniform hypergraph on $n$ vertices and of minimum codegree at least $n /2 + o (n)$ contains every spanning tight $k$ -tree of bounded vertex degre…

math.CO2020

Universal arrays

Matías Pavez-Signé, Daniel A. Quiroz, Nicolás Sanhueza-Matamala

A word on $q$ symbols is a sequence of letters from a fixed alphabet of size $q$ . For an integer $k \geq 1$ , we say that a word $w$ is $k$ -universal if, given an arbitrary word of le…