Alberto Espuny Díaz

activity

20182020

collaborators

5 papers

math.CO2020

Hamiltonicity of random subgraphs of the hypercube

Padraig Condon, Alberto Espuny Díaz, António Girão +2

We study Hamiltonicity in random subgraphs of the hypercube $Q^{n}$ . Our first main theorem is an optimal hitting time result. Consider the random process which includes th…

math.CO2019

Dirac's theorem for random regular graphs

Padraig Condon, Alberto Espuny Díaz, António Girão +2

We prove a `resilience' version of Dirac's theorem in the setting of random regular graphs. More precisely, we show that, whenever $d$ is sufficiently large compared to $\varepsilo…

math.CO2018

Resilient degree sequences with respect to Hamilton cycles and matchings in random graphs

Padraig Condon, Alberto Espuny Díaz, Jaehoon Kim +2

Pósa's theorem states that any graph $G$ whose degree sequence $d_{1} \leq \dots \leq d_{n}$ satisfies $d_{i} \geq i + 1$ for all $i < n /2$ has a Hamilton cycle. This degree condition is bes…

math.CO2018

Entropy versions of additive inequalities

Alberto Espuny Díaz, Oriol Serra

The connection between inequalities in additive combinatorics and analogous versions in terms of the entropy of random variables has been extensively explored over the past few yea…

math.CO2018

Edge correlations in random regular hypergraphs and applications to subgraph testing

Alberto Espuny Díaz, Felix Joos, Daniela Kühn +1

Compared to the classical binomial random (hyper)graph model, the study of random regular hypergraphs is made more challenging due to correlations between the occurrence of differe…