Thomassen’s conjecture for line graphs of 3-hypergraphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F20%3A43957823" target="_blank" >RIV/49777513:23520/20:43957823 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0012365X20300297?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0012365X20300297?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.disc.2020.111838" target="_blank" >10.1016/j.disc.2020.111838</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Thomassen’s conjecture for line graphs of 3-hypergraphs

Popis výsledku v původním jazyce

In 1986, Thomassen conjectured that every 4-connected line graph is hamiltonian. The conjecture is still wide open, and, as a possible approach to it, many statements that are equivalent or related to it have been studied. In this paper, we extend the statement to the class of line graphs of 3-hypergraphs, and generalize it to Tutte cycles and paths. Among others, we formulate the following conjectures: (i) every 2-connected line graph of a 3-hypergraph has a Tutte maximal cycle containing any two prescribed vertices, (ii) every 3-connected line graph of a 3-hypergraph has a Tutte maximal cycle containing any three prescribed vertices, (iii) every connected line graph of a 3-hypergraph has a Tutte maximal (a, b)-path for any two vertices a, b, (iv) every 4-connected line graph of a 3-hypergraph is Hamilton-connected, and we show that all these (seemingly much stronger) statements are equivalent with Thomassen’s conjecture.

Název v anglickém jazyce

Thomassen’s conjecture for line graphs of 3-hypergraphs

Popis výsledku anglicky

In 1986, Thomassen conjectured that every 4-connected line graph is hamiltonian. The conjecture is still wide open, and, as a possible approach to it, many statements that are equivalent or related to it have been studied. In this paper, we extend the statement to the class of line graphs of 3-hypergraphs, and generalize it to Tutte cycles and paths. Among others, we formulate the following conjectures: (i) every 2-connected line graph of a 3-hypergraph has a Tutte maximal cycle containing any two prescribed vertices, (ii) every 3-connected line graph of a 3-hypergraph has a Tutte maximal cycle containing any three prescribed vertices, (iii) every connected line graph of a 3-hypergraph has a Tutte maximal (a, b)-path for any two vertices a, b, (iv) every 4-connected line graph of a 3-hypergraph is Hamilton-connected, and we show that all these (seemingly much stronger) statements are equivalent with Thomassen’s conjecture.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

DISCRETE MATHEMATICS

ISSN

0012-365X

e-ISSN

—

Svazek periodika

343

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

18

Strana od-do

—

Kód UT WoS článku

000528203800018

EID výsledku v databázi Scopus

2-s2.0-85079170994