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math.CO2026
A minimum-degree threshold for colour-biased Hamilton cycles in hypergraphs
Natalie Behague, Felix Christian Clemen, Joseph Hyde +1
We determine the asymptotically best possible minimum vertex degree condition forcing a two-coloured -graph to contain a colour-biased tight Hamilton cycle. This confirms a conj…
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 is a graph with minimum degree at least then has a Hamilton cycle. A natural generalisation asks what properties of an ed…