Sparse Kneser graphs are Hamiltonian

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10435478" target="_blank" >RIV/00216208:11320/21:10435478 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=9NehUl4amW" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=9NehUl4amW</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1112/jlms.12406" target="_blank" >10.1112/jlms.12406</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Sparse Kneser graphs are Hamiltonian

Popis výsledku v původním jazyce

For integers k &gt; 1 and n &gt; 2k+1, the Kneser graph K(n,k) is the graph whose vertices are the k-element subsets of {1,...,n} and whose edges connect pairs of subsets that are disjoint. The Kneser graphs of the form K(2k+1,k) are also known as the odd graphs. We settle an old problem due to Meredith, Lloyd, and Biggs from the 1970s, proving that for every k &gt; 3, the odd graph K(2k+1,k) has a Hamilton cycle. This and a known conditional result due to Johnson imply that all Kneser graphs of the form K(2k+2a,k) with k &gt; 3 and a &gt; 0 have a Hamilton cycle. We also prove that K(2k+1,k) has at least 22k-6 distinct Hamilton cycles for k &gt; 6. Our proofs are based on a reduction of the Hamiltonicity problem in the odd graph to the problem of finding a spanning tree in a suitably defined hypergraph on Dyck words.

Název v anglickém jazyce

Sparse Kneser graphs are Hamiltonian

Popis výsledku anglicky

For integers k &gt; 1 and n &gt; 2k+1, the Kneser graph K(n,k) is the graph whose vertices are the k-element subsets of {1,...,n} and whose edges connect pairs of subsets that are disjoint. The Kneser graphs of the form K(2k+1,k) are also known as the odd graphs. We settle an old problem due to Meredith, Lloyd, and Biggs from the 1970s, proving that for every k &gt; 3, the odd graph K(2k+1,k) has a Hamilton cycle. This and a known conditional result due to Johnson imply that all Kneser graphs of the form K(2k+2a,k) with k &gt; 3 and a &gt; 0 have a Hamilton cycle. We also prove that K(2k+1,k) has at least 22k-6 distinct Hamilton cycles for k &gt; 6. Our proofs are based on a reduction of the Hamiltonicity problem in the odd graph to the problem of finding a spanning tree in a suitably defined hypergraph on Dyck words.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/GA19-08554S" target="_blank" >GA19-08554S: Struktury a algoritmy ve velmi symetrických grafech</a><br>

Návaznosti

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

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Journal of the London Mathematical Society

ISSN

0024-6107

e-ISSN

—

Svazek periodika

103

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

23

Strana od-do

1253-1275

Kód UT WoS článku

000597234900001

EID výsledku v databázi Scopus

2-s2.0-85097370090