Mat'ias Pavez-Sign'e

collaborators

6 papers

math.CO2026

Spanning clique subdivisions in pseudorandom graphs

Hyunwoo Lee, MatÃas Pavez-SignÃ©, Teo Petrov

In this paper, we study the appearance of a spanning subdivision of a clique in graphs satisfying certain pseudorandom conditions. Specifically, we show the following three results…

math.CO2026

Ramsey numbers for 1-degenerate 3-graphs

Peter Allen, Simona Boyadzhiyska, MatÃas Pavez-SignÃ©

We construct a 3-uniform 1-degenerate hypergraph on $n$ vertices whose 2-colour Ramsey number is $I^c ◯ (n^{3/2} / lo g n)$ . This shows that all remaining open cases of the hyper…

math.CO2026

The LovÃ¡sz conjecture holds for moderately dense Cayley graphs

Benjamin Bedert, Nemanja DraganiÄ, Alp MÃ¼yesser +1

We show that there is an absolute constant $c > 0$ such that every large connected $n$ -vertex Cayley graph with degree $d \geq n^{1 - c}$ has a Hamilton cycle. This makes progress towar…

math.CO2025

Ramsey numbers of trees

Richard Montgomery, MatÃas Pavez-SignÃ©, Jun Yan

We show that there exists a constant $c > 0$ such that every $n$ -vertex tree $T$ with $I^ (T) \leq c n$ has Ramsey number $R (T) = max {t_{1} + 2 t_{2}, 2 t_{1}} - 1$ , where $t_{1} \geq t_{2}$ are the sizes…

math.CO2025

Hamilton cycles in pseudorandom graphs: resilience and approximate decompositions

Nemanja DraganiÄ, Jaehoon Kim, Hyunwoo Lee +3

Dirac's classical theorem asserts that, for $n \geq 3$ , any $n$ -vertex graph with minimum degree at least $n /2$ is Hamiltonian. Furthermore, if we additionally assume that such grap…

math.CO2025

Colour-bias perfect matchings in hypergraphs

HiÃªp HÃ n, Richard Lang, JoÃ£o 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…