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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

We establish an inclusion relation between two uniform models of random k-graphs (for constant k &gt;= 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 &lt;&lt; m &lt;&lt; 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 -&gt; infinity. This extends an earlier result of Kim and Vu about &quot;sandwiching random graphs&quot;. 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 &gt;= 3 we conclude that if n(k-2) &lt;&lt; d &lt;&lt; n(k-1), then a.a.s. R-(k)(n, d) contains a tight Hamilton cycle.

Název v anglickém jazyce

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

Popis výsledku anglicky

We establish an inclusion relation between two uniform models of random k-graphs (for constant k &gt;= 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 &lt;&lt; m &lt;&lt; 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 -&gt; infinity. This extends an earlier result of Kim and Vu about &quot;sandwiching random graphs&quot;. 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 &gt;= 3 we conclude that if n(k-2) &lt;&lt; d &lt;&lt; n(k-1), then a.a.s. R-(k)(n, d) contains a tight Hamilton cycle.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Journal of Combinatorial Theory. Series B

ISSN

0095-8956

e-ISSN

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Svazek periodika

122

Číslo periodika v rámci svazku

January

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

719-740

Kód UT WoS článku

000389788300033

EID výsledku v databázi Scopus

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