Padraig Condon

collaborators

2 papers

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…