Finding tight hamilton cycles in random hypergraphs faster

Allen, Peter ORCID: 0000-0001-6555-3501, Koch, Christoph, Parczyk, Olaf and Person, Yury (2018) Finding tight hamilton cycles in random hypergraphs faster. In: Bender, M., Farach-Colton, M. and Mosteiro, M., (eds.) LATIN 2018: theoretical informatics. Lecture Notes in Computer Science (10807). Springer Berlin / Heidelberg, Cham, Switzerland, pp. 28-36. ISBN 9783319774039

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Abstract

In an r-uniform hypergraph on n vertices a tight Hamilton cycle consists of n edges such that there exists a cyclic ordering of the vertices where the edges correspond to consecutive segments of r vertices. We provide a first deterministic polynomial time algorithm, which finds a.a.s. tight Hamilton cycles in random r-uniform hypergraphs with edge probability at least Clog3n/n . Our result partially answers a question of Dudek and Frieze (Random Struct Algorithms 42:374–385, 2013) who proved that tight Hamilton cycles exists already for p=ω(1/n) for r=3 and p=(e+o(1))/n for r≥4 using a second moment argument. Moreover our algorithm is superior to previous results of Allen et al. (Random Struct Algorithms 46:446–465, 2015) and Nenadov and Škorić (arXiv:1601.04034) in various ways: the algorithm of Allen et al. is a randomised polynomial time algorithm working for edge probabilities p≥n−1+ε , while the algorithm of Nenadov and Škorić is a randomised quasipolynomial time algorithm working for edge probabilities p≥Clog8n/n .

Item Type:	Book Section
Official URL:	https://link.springer.com/book/10.1007/978-3-319-7...
Additional Information:	© 2018 Springer International Publishing AG, part of Springer Nature
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	18 May 2018 10:24
Last Modified:	01 Oct 2024 03:59
Projects:	P26826, 639046, PE 2299/1-1
Funders:	Austrian Science Fund, European Research Council, DFG grant
URI:	http://eprints.lse.ac.uk/id/eprint/88000

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