Powers of Hamiltonian cycles in multipartite graphs

Powers of Hamiltonian cycles in multipartite graphs

We prove that if G is a k-partite graph on n vertices in which all of the parts have order at most n/r and every vertex is adjacent to at least a 1−1/r+o(1) proportion of the vertices in every other part, then G contains the (r−1)-st power of a Hamiltonian cycle.

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Discrete mathematics 2022-04, Vol.345 (4), p.112747, Article 112747
Hauptverfasser: DeBiasio, Louis, Martin, Ryan R., Molla, Theodore
Format: Artikel
Sprache:eng
Schlagworte:
Absorbing
Extremal embedding problems
Multipartite
Powers of Hamiltonian cycles
Regularity
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We prove that if G is a k-partite graph on n vertices in which all of the parts have order at most n/r and every vertex is adjacent to at least a 1−1/r+o(1) proportion of the vertices in every other part, then G contains the (r−1)-st power of a Hamiltonian cycle.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2021.112747