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STACS
2016
Springer

The Complexity of the Hamilton Cycle Problem in Hypergraphs of High Minimum Codegree

4 years 3 months ago
The Complexity of the Hamilton Cycle Problem in Hypergraphs of High Minimum Codegree
We consider the complexity of the Hamilton cycle decision problem when restricted to k-uniform hypergraphs H of high minimum codegree δ(H). We show that for tight Hamilton cycles this problem is NP-hard even when restricted to k-uniform hypergraphs H with δ(H) ≥ n 2 −C, where n is the order of H and C is a constant which depends only on k. This answers a question raised by Karpiński, Ruciński and Szymańska. Additionally we give a polynomial-time algorithm which, for a sufficiently small constant ε > 0, determines whether or not a 4-uniform hypergraph H on n vertices with δ(H) ≥ n 2 − εn contains a Hamilton 2-cycle. This demonstrates that some looser Hamilton cycles exhibit interestingly different behaviour compared to tight Hamilton cycles. A key part of the proof is a precise characterisation of all 4-uniform hypergraphs H on n vertices with δ(H) ≥ n 2 −εn which do not contain a Hamilton 2-cycle; this may be of independent interest. As an additional corollar...
Frederik Garbe, Richard Mycroft
Added 10 Apr 2016
Updated 10 Apr 2016
Type Journal
Year 2016
Where STACS
Authors Frederik Garbe, Richard Mycroft
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