Localized Codegree Conditions for Tight Hamilton Cycles in 3-Uniform Hypergraphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F22%3A00556853" target="_blank" >RIV/67985807:_____/22:00556853 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/21M1408531" target="_blank" >http://dx.doi.org/10.1137/21M1408531</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/21M1408531" target="_blank" >10.1137/21M1408531</a>
Alternative languages
Result language
angličtina
Original language name
Localized Codegree Conditions for Tight Hamilton Cycles in 3-Uniform Hypergraphs
Original language description
We study sufficient conditions for the existence of Hamilton cycles in uniformly dense 3-uniform hypergraphs. Problems of this type were first considered by Lenz, Mubayi, and Mycroft for loose Hamilton cycles, and Aigner-Horev and Levy considered them for tight Hamilton cycles for a fairly strong notion of uniformly dense hypergraphs. We focus on tight cycles and obtain optimal results for a weaker notion of uniformly dense hypergraphs. We show that if an n-vertex 3-uniform hypergraph H = (V, E) has the property that for any set of vertices X and for any collection P of pairs of vertices, the number of hyperedges composed by a pair belonging to P and one vertex from X is at least (1/4 +o(1))vertical bar X vertical bar vertical bar P vertical bar- o(vertical bar V vertical bar(3)) and H has minimum vertex degree at least Omega(vertical bar V vertical bar(2)), then H contains a tight Hamilton cycle. A probabilistic construction shows that the constant 1/4 is optimal in this context.
Czech name
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Czech description
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Classification
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
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Discrete Mathematics
ISSN
0895-4801
e-ISSN
1095-7146
Volume of the periodical
36
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
23
Pages from-to
147-169
UT code for WoS article
000778502000008
EID of the result in the Scopus database
2-s2.0-85128397699