Hamilton cycles in sparse locally connected graphs

Hamilton cycles in sparse locally connected graphs

A graph G is locally connected if for every v∈V(G) the open neighbourhood N(v) of v is nonempty and induces a connected graph in G. We characterize locally connected graphs of order n with less than 2n edges and show that for any natural number k the Hamilton Cycle Problem for locally connected grap...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Discrete Applied Mathematics 2019-03, Vol.257, p.276-288
Hauptverfasser: van Aardt, Susan A., Burger, Alewyn P., Frick, Marietjie, Thomassen, Carsten, de Wet, Johan P.
Format: Artikel
Sprache:eng
Schlagworte:
Graphs
Hamiltonian
Locally connected
NP-complete
Polynomial time algorithm
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:A graph G is locally connected if for every v∈V(G) the open neighbourhood N(v) of v is nonempty and induces a connected graph in G. We characterize locally connected graphs of order n with less than 2n edges and show that for any natural number k the Hamilton Cycle Problem for locally connected graphs of order n with m edges is polynomially solvable if m≤2n+klog2n, but NP-complete if m=2n+⌊n1∕k⌋.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2018.10.031