Embedding the Erdos-Renyi hypergraph into the random regular hypergraph and Hamiltonicity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10360349" target="_blank" >RIV/00216208:11320/17:10360349 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jctb.2016.09.003" target="_blank" >http://dx.doi.org/10.1016/j.jctb.2016.09.003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jctb.2016.09.003" target="_blank" >10.1016/j.jctb.2016.09.003</a>

Result language
angličtina
Original language name
Embedding the Erdos-Renyi hypergraph into the random regular hypergraph and Hamiltonicity
Original language description
We establish an inclusion relation between two uniform models of random k-graphs (for constant k >= 2) on n labeled vertices: G((k)) (n, m), the random k-graph with m edges, and R-(k) (n, d), the random d-regular k-graph. We show that if n log n << m << n(k) we can choose d = d(n) similar to km/n and couple G((k)) (n, m) and R-(k) (n, d) so that the latter contains the former with probability tending to one as n -> infinity. This extends an earlier result of Kim and Vu about "sandwiching random graphs". In view of known threshold theorems on the existence of different types of Hamilton cycles in G((k))(n, m), our result allows us to find conditions under which R-(k)(n, d) is Hamiltonian. In particular, for k >= 3 we conclude that if n(k-2) << d << n(k-1), then a.a.s. R-(k)(n, d) contains a tight Hamilton cycle.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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