Camila Z'arate-Guer'en

collaborators

4 papers

math.CO2025

Positive codegree thresholds for perfect matchings in hypergraphs

Richard Mycroft, Camila Zárate-Guerén

We give, for each $k \geq 3$ , the precise best possible minimum positive codegree condition for a perfect matching in a large $k$ -uniform hypergraph $H$ on $n$ vertices. Specifical…

math.CO2025

Positive codegree thresholds for Hamilton cycles in hypergraphs

Richard Mycroft, Camila Zárate-Guerén

For each $k \geq 3$ and $1 \leq ℓ \leq k - 1$ we give an asymptotically best possible minimum positive codegree condition for the existence of a Hamilton $ℓ$ -cycle in a $k$ -uni…

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.CO2024

A note on colour-bias perfect matchings in hypergraphs

József Balogh, Andrew Treglown, Camila Zárate-Guerén

A result of Balogh, Csaba, Jing and Pluhár yields the minimum degree threshold that ensures a $2$ -coloured graph contains a perfect matching of significant colour-bias (i.e., a per…