Nicolás Sanhueza-Matamala

activity

20172026

most citedCovering and tiling hypergraphs with tight cycles

8 citations · 22 across the 22 of their papers we have counts for

collaborators

25 papers

math.CO2026

The asymptotic version of the Erdős-Sós conjecture and beyond

Akbar Davoodi, Diana Piguet, Hanka Řada +1

Klimošová, Piguet, and Rozhoň conjectured that any graph with minimum degree $k /2$ and sufficiently many vertices of degree $k$ should contain all trees with $k$ edges. We prove an…

math.CO2025

Loose Hamiltonicity

Richard Lang, Nicolás Sanhueza-Matamala

We study the appearance of Hamilton $ℓ$ -cycles in dense $k$ -uniform hypergraphs when $ℓ \leq k - 2$ and $k - ℓ$ does not divide $k$ . Our main result reduces this problem to th…

math.CO2025

Optimal and Efficient Partite Decompositions of Hypergraphs

Andrew Krapivin, Benjamin Przybocki, Nicolás Sanhueza-Matamala +1

We study the problem of partitioning the edges of a $d$ -uniform hypergraph $H$ into a family $F$ of complete $d$ -partite hypergraphs ( $d$ -cliques). We show that there is a partitio…

math.CO2025

Degree conditions for spanning expansion hypertrees

Mengjiao Rao, Nicolás Sanhueza-Matamala, Lin Sun +2

The $k$ -expansion of a graph $G$ is the $k$ -uniform hypergraph obtained from $G$ by adding $k - 2$ new vertices to every edge. We determine, for all $k > d \geq 1$ , asymptotically op…

math.CO2024

Blowing up Dirac's theorem

Richard Lang, Nicolás Sanhueza-Matamala

We show that every graph $G$ on $n$ vertices with $δ (G) \geq (1/2 + ε) n$ is spanned by a complete blow-up of a cycle with clusters of nearly uniform size $Ω (lo g n)$ . The p…

math.CO2024

A hypergraph bandwidth theorem

Richard Lang, Nicolás Sanhueza-Matamala

A cornerstone of extremal graph theory due to Erdős and Stone states that the edge density which guarantees a fixed graph $F$ as subgraph also asymptotically guarantees a blow-up o…

math.CO2024

The codegree Turán density of $3$ -uniform tight cycles

Simón Piga, Nicolás Sanhueza-Matamala, Mathias Schacht

Given any $ε > 0$ we prove that every sufficiently large $n$ -vertex $3$ -graph $H$ where every pair of vertices is contained in at least $(1/3 + ε) n$ edges contains…

math.CO2024

Vertex-separating path systems in random graphs

Lyuben Lichev, Nicolás Sanhueza-Matamala

A set $V$ is said to be separated by subsets $V_{1}, \dots, V_{k}$ if, for every pair of distinct elements of $V$ , there is a set $V_{i}$ that contains exactly one of them. Imposing struc…

math.CO2024

Colour-bias perfect matchings in hypergraphs

Hiêp Hàn, Richard Lang, João Pedro Marciano +4

We study conditions under which an edge-coloured hypergraph has a particular substructure that contains more than the trivially guaranteed number of monochromatic edges. Our main r…

math.CO2023★ 1 cited

Separating path systems in complete graphs

Cristina G. Fernandes, Guilherme Oliveira Mota, Nicolás Sanhueza-Matamala

We prove that in any $n$ -vertex complete graph there is a collection $P$ of $(1 + o (1)) n$ paths that strongly separates any pair of distinct edges $e, f$ , meaning that th…

math.CO2023★ 1 cited

Robust Hamiltonicity

Felix Joos, Richard Lang, Nicolás Sanhueza-Matamala

We study conditions under which a given hypergraph is randomly robust Hamiltonian, which means that a random sparsification of the host graph contains a Hamilton cycle with high pr…

math.CO2023★ 1 cited

Separating path systems in trees

Francisco Arrepol, Patricio Asenjo, Raúl Astete +6

For a graph $G$ , an edge-separating (resp. vertex-separating) path system of $G$ is a family of paths in $G$ such that for any pair of edges $e_{1}, e_{2}$ (resp. pair of vertices $v_1…

math.CO2022

Cycle decompositions in $k$ -uniform hypergraphs

Allan Lo, Simón Piga, Nicolás Sanhueza-Matamala

We show that $k$ -uniform hypergraphs on $n$ vertices whose codegree is at least $(2/3 + o (1)) n$ can be decomposed into tight cycles, subject to the trivial divisibility conditions.…

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

On sufficient conditions for spanning structures in dense graphs

Richard Lang, Nicolás Sanhueza-Matamala

We study structural conditions in dense graphs that guarantee the existence of vertex-spanning substructures such as Hamilton cycles. It is easy to see that every Hamiltonian graph…

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.CO2021★ 2 cited

Cycle decompositions in $3$ -uniform hypergraphs

Simón Piga, Nicolás Sanhueza-Matamala

We show that $3$ -graphs on $n$ vertices whose codegree is at least $(2/3 + o (1)) n$ can be decomposed into tight cycles and admit Euler tours, subject to the trivial necessary divis…

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

Minimum degree conditions for tight Hamilton cycles

Richard Lang, Nicolás Sanhueza-Matamala

We develop a new framework to study minimum $d$ -degree conditions in $k$ -uniform hypergraphs, which guarantee the existence of a tight Hamilton cycle. Our main theoretical result d…

math.CO2020

Longest paths in random hypergraphs

Oliver Cooley, Frederik Garbe, Eng Keat Hng +3

Given integers $k, j$ with $1 \leq j \leq k - 1$ , we consider the length of the longest $j$ -tight path in the binomial random $k$ -uniform hypergraph $H^{k} (n, p)$ . We show that this length…

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…

math.CO2018

Density of monochromatic infinite paths

Allan Lo, Nicolás Sanhueza-Matamala, Guanghui Wang

For any subset $A \subseteq N$ , we define its upper density to be $lim sup_{n \to \infty} ∣ A \cap {1, \dots, n} ∣/ n$ . We prove that every $2$ -edge-colourin…

math.CO2017★ 7 cited

An asymptotic bound for the strong chromatic number

Allan Lo, Nicolás Sanhueza-Matamala

The strong chromatic number $χ_{s} (G)$ of a graph $G$ on $n$ vertices is the least number $r$ with the following property: after adding $r ⌈ n / r ⌉ - n$ isolated ve…

The asymptotic version of the Erdős-Sós conjecture and beyond

Loose Hamiltonicity

Optimal and Efficient Partite Decompositions of Hypergraphs

Degree conditions for spanning expansion hypertrees

Blowing up Dirac's theorem

A hypergraph bandwidth theorem

The codegree Turán density of 3-uniform tight cycles

Vertex-separating path systems in random graphs

Colour-bias perfect matchings in hypergraphs

Separating path systems in complete graphs

Robust Hamiltonicity

Separating path systems in trees

Cycle decompositions in k-uniform hypergraphs

Ramsey numbers with prescribed rate of growth

Ramsey numbers of cycles in random graphs

On sufficient conditions for spanning structures in dense graphs

Towards a hypergraph version of the Pósa-Seymour conjecture

Cycle decompositions in 3-uniform hypergraphs

Dirac-type conditions for spanning bounded-degree hypertrees

Minimum degree conditions for tight Hamilton cycles

Longest paths in random hypergraphs

Universal arrays

Density of monochromatic infinite paths

An asymptotic bound for the strong chromatic number

The codegree Turán density of $3$ -uniform tight cycles

Cycle decompositions in $k$ -uniform hypergraphs

Cycle decompositions in $3$ -uniform hypergraphs