Allan Lo

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20172026

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math.CO2026

Towards Pósa's Conjecture for $3$ -graphs

Debmalya Bandyopadhyay, Allan Lo, Richard Mycroft

We prove that every $3$ -graph $H$ on $n$ vertices with minimum codegree $δ_{2} (H) \geq 7 n /9 + o (n)$ contains the square of a tight Hamilton cycle. This strengthens a theorem of Beden…

math.CO2026

Compatible Hamilton cycles in graphs with large minimum degree

Natalie Behague, Francesco Di Braccio, Bertille Granet +1

The renowned theorem of Dirac states that if $G$ is a graph with minimum degree at least $n /2$ then $G$ has a Hamilton cycle. A natural generalisation asks what properties of an ed…

Towards Pósa's Conjecture for 3-graphs

Compatible Hamilton cycles in graphs with large minimum degree

Towards Pósa's Conjecture for $3$ -graphs