Nordhaus-Gaddum Results for the Sum of the Induced Path Number of a Graph and Its Complement

Nordhaus-Gaddum Results for the Sum of the Induced Path Number of a Graph and Its Complement

The induced path number p（G） of a graph G is defined as the minimum number of subsets into which the vertex set of G can be partitioned so that each subset induces a path. Broere et hi. proved that if G is a graph of order n, then 〈 p（G） ＋ p（G） 〈3n/2] . In this paper,_we characterize [3n/2], improve...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Acta mathematica Sinica. English series 2012-12, Vol.28 (12), p.2365-2372
Hauptverfasser: Hattingh, Johannes H., Saleh, Ossama A., van Der Merwe, Lucas C., Walters, Terry J.
Format: Artikel
Sprache:eng
Schlagworte:
Complement
Graph theory
Graphs
Integers
Lower bounds
Mathematical analysis
Mathematics
Mathematics and Statistics
Studies
Upper bounds
子集
形数
整数
最小数
诱导
路径数
顶点集
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:The induced path number p（G） of a graph G is defined as the minimum number of subsets into which the vertex set of G can be partitioned so that each subset induces a path. Broere et hi. proved that if G is a graph of order n, then 〈 p（G） ＋ p（G） 〈3n/2] . In this paper,_we characterize [3n/2], improve the lower bound on p（G） ＋ p（G） by one when the graphs G for which p（G） -4- p（G） = 3n n is the square of an odd integer, and determine a best possible upper bound for p（G） ＋ p（G） when neither G nor G has isolated vertices.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-012-0727-6