Degree Conditions Forcing Directed Cycles

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F23%3A00365664" target="_blank" >RIV/68407700:21340/23:00365664 - isvavai.cz</a>

Výsledek na webu

<a href="http://hdl.handle.net/10467/108535" target="_blank" >http://hdl.handle.net/10467/108535</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1093/imrn/rnac114" target="_blank" >10.1093/imrn/rnac114</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Degree Conditions Forcing Directed Cycles

Popis výsledku v původním jazyce

Caccetta-Haggkvist conjecture is a longstanding open problem on degree conditions that force an oriented graph to contain a directed cycle of a bounded length. Motivated by this conjecture, Kelly, Kuhn, and Osthus initiated a study of degree conditions forcing the containment of a directed cycle of a given length. In particular, they found the optimal minimum semidegree, that is, the smaller of the minimum indegree and the minimum outdegree, which forces a large oriented graph to contain a directed cycle of a given length not divisible by 3, and conjectured the optimal minimum semidegree for all the other cycles except the directed triangle. In this paper, we establish the best possible minimum semidegree that forces a large oriented graph to contain a directed cycle of a given length divisible by 3 yet not equal to 3, hence fully resolve the conjecture by Kelly, Kuhn, and Osthus. We also find an asymptotically optimal semidegree threshold of any cycle with a given orientation of its edges with the sole exception of a directed triangle.

Název v anglickém jazyce

Degree Conditions Forcing Directed Cycles

Popis výsledku anglicky

Caccetta-Haggkvist conjecture is a longstanding open problem on degree conditions that force an oriented graph to contain a directed cycle of a bounded length. Motivated by this conjecture, Kelly, Kuhn, and Osthus initiated a study of degree conditions forcing the containment of a directed cycle of a given length. In particular, they found the optimal minimum semidegree, that is, the smaller of the minimum indegree and the minimum outdegree, which forces a large oriented graph to contain a directed cycle of a given length not divisible by 3, and conjectured the optimal minimum semidegree for all the other cycles except the directed triangle. In this paper, we establish the best possible minimum semidegree that forces a large oriented graph to contain a directed cycle of a given length divisible by 3 yet not equal to 3, hence fully resolve the conjecture by Kelly, Kuhn, and Osthus. We also find an asymptotically optimal semidegree threshold of any cycle with a given orientation of its edges with the sole exception of a directed triangle.

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

2023

Kód důvěrnosti údajů

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

Název periodika

International Mathematics Research Notices

ISSN

1073-7928

e-ISSN

1687-0247

Svazek periodika

2023

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

43

Strana od-do

9711-9753

Kód UT WoS článku

000797059000001

EID výsledku v databázi Scopus

2-s2.0-85163052902