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Minimum vertex degree threshold for loose Hamilton cycles in 3-uniform hypergraphs (1307.3693v2)
Published 14 Jul 2013 in math.CO
Abstract: We show that for sufficiently large $n$, every 3-uniform hypergraph on $n$ vertices with minimum vertex degree at least $\binom{n-1}2 - \binom{\lfloor\frac34 n\rfloor}2 + c$, where $c=2$ if $n\in 4\mathbb{N}$ and $c=1$ if $n\in 2\mathbb{N}\setminus 4\mathbb{N}$, contains a loose Hamilton cycle. This degree condition is best possible and improves on the work of Bu\ss, H`an and Schacht who proved the corresponding asymptotical result.