Hamilton cycles in hypergraphs below the Dirac threshold

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00493792" target="_blank" >RIV/67985840:_____/18:00493792 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jctb.2018.04.010" target="_blank" >http://dx.doi.org/10.1016/j.jctb.2018.04.010</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jctb.2018.04.010" target="_blank" >10.1016/j.jctb.2018.04.010</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Hamilton cycles in hypergraphs below the Dirac threshold

Popis výsledku v původním jazyce

We establish a precise characterisation of 4-uniform hypergraphs with minimum codegree close to n/2 which contain a Hamilton 2-cycle. As an immediate corollary we identify the exact Dirac threshold for Hamilton 2-cycles in 4-uniform hypergraphs. Moreover, by derandomising the proof of our characterisation we provide a polynomial-time algorithm which, given a 4-uniform hypergraph H with minimum codegree close to n/2, either finds a Hamilton 2-cycle in H or provides a certificate that no such cycle exists. This surprising result stands in contrast to the graph setting, in which below the Dirac threshold it is NP-hard to determine if a graph is Hamiltonian. We also consider tight Hamilton cycles in k-uniform hypergraphs H for k≥3, giving a series of reductions to show that it is NP-hard to determine whether a k-uniform hypergraph H with minimum degree δ(H)≥[Formula presented]|V(H)|−O(1) contains a tight Hamilton cycle.

Název v anglickém jazyce

Hamilton cycles in hypergraphs below the Dirac threshold

Popis výsledku anglicky

We establish a precise characterisation of 4-uniform hypergraphs with minimum codegree close to n/2 which contain a Hamilton 2-cycle. As an immediate corollary we identify the exact Dirac threshold for Hamilton 2-cycles in 4-uniform hypergraphs. Moreover, by derandomising the proof of our characterisation we provide a polynomial-time algorithm which, given a 4-uniform hypergraph H with minimum codegree close to n/2, either finds a Hamilton 2-cycle in H or provides a certificate that no such cycle exists. This surprising result stands in contrast to the graph setting, in which below the Dirac threshold it is NP-hard to determine if a graph is Hamiltonian. We also consider tight Hamilton cycles in k-uniform hypergraphs H for k≥3, giving a series of reductions to show that it is NP-hard to determine whether a k-uniform hypergraph H with minimum degree δ(H)≥[Formula presented]|V(H)|−O(1) contains a tight Hamilton cycle.

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

2018

Kód důvěrnosti údajů

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

Název periodika

Journal of Combinatorial Theory. B

ISSN

0095-8956

e-ISSN

—

Svazek periodika

133

Číslo periodika v rámci svazku

November

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

58

Strana od-do

153-210

Kód UT WoS článku

000448095200008

EID výsledku v databázi Scopus

2-s2.0-85046770002