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arXiv · 1603.04462

Minimum vertex degree conditions for loose Hamilton cycles in $3$-uniform hypergraphs

E. Buß·H. Hàn·M. Schacht
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Abstract

We investigate minimum vertex degree conditions for $3$-uniform hypergraphs which ensure the existence of loose Hamilton cycles. A loose Hamilton cycle is a spanning cycle in which only consecutive edges intersect and these intersections consist of precisely one vertex. We prove that every $3$-uniform $n$-vertex ($n$ even) hypergraph $\mathcal{H}$ with minimum vertex degree $\delta_1(\mathcal{H})\geq \left(\frac7{16}+o(1)\right)\binom{n}{2}$ contains a loose Hamilton cycle. This bound is asymptotically best possible.

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E. Buß, H. Hàn, M. Schacht. 2016-03-14. Minimum vertex degree conditions for loose Hamilton cycles in $3$-uniform hypergraphs. https://doi.org/10.1016/j.jctb.2013.07.004

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