Matías Pavez-Signé

activity

20232026

collaborators

6 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

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

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…