Localized Codegree Conditions for Tight Hamilton Cycles in 3-Uniform Hypergraphs

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Localized Codegree Conditions for Tight Hamilton Cycles in 3-Uniform Hypergraphs

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Localized Codegree Conditions for Tight Hamilton Cycles in 3-Uniform Hypergraphs

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

SIAM Journal on Discrete Mathematics

ISSN

0895-4801

e-ISSN

1095-7146

Svazek periodika

36

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

23

Strana od-do

147-169

Kód UT WoS článku

000778502000008

EID výsledku v databázi Scopus

2-s2.0-85128397699