Loose Hamiltonian cycles forced by large \((k-2)\)-degree – sharp version. (English) Zbl 1378.05151
Drmota, Michael (ed.) et al., Extended abstracts of the ninth European conference on combinatorics, graph theory and applications, EuroComb 2017, Vienna, Austria, August 28 – September 1, 2017. Amsterdam: Elsevier. Electronic Notes in Discrete Mathematics 61, 101-106 (2017).
Summary: We prove for all \(k \geqslant 4\) and \(1 \leqslant\ell<k/2\) the sharp minimum \((k-2)\)-degree bound for a \(k\)-uniform hypergraph \(\mathcal H\) on \(n\) vertices to contain a Hamiltonian \(\ell\)-cycle if \(k- \ell\) divides \(n\) and \(n\) is sufficiently large. This extends a result of J. Han and Y. Zhao [J. Comb. Theory, Ser. B 114, 70–96 (2015; Zbl 1315.05095)] for 3-uniform hypergraphs.
For the entire collection see [Zbl 1375.05004].
For the entire collection see [Zbl 1375.05004].
Citations:
Zbl 1315.05095References:
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