Padraig Condon

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20172020

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4 papers · 1 filter

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.CO2017

A bandwidth theorem for approximate decompositions

Padraig Condon, Jaehoon Kim, Daniela Kühn +1

We provide a degree condition on a regular $n$ -vertex graph $G$ which ensures the existence of a near optimal packing of any family $H$ of bounded degree $n$ -vertex $k$ -ch…