A new family of layer barriers for colour-biased tight Hamilton cycles gives a counterexample to the recent conjecture of Behague, Clemen, Hyde and Morrison on minimum vertex degree thresholds.
A minimum-degree threshold for colour-biased Hamilton cycles in hypergraphs
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abstract
We determine the asymptotically best possible minimum vertex degree condition forcing a two-coloured $3$-graph to contain a colour-biased tight Hamilton cycle. This confirms a conjecture of H\`an, Lang, Marciano, Pavez-Sign\'e, Sanhueza-Matamala, Treglown and Z\'arate-Guer\'en.
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Layer barriers for colour-biased tight Hamilton cycles
A new family of layer barriers for colour-biased tight Hamilton cycles gives a counterexample to the recent conjecture of Behague, Clemen, Hyde and Morrison on minimum vertex degree thresholds.