INDEPENDENT DOMINATION is one of the rare problems for which the complexity of weighted and unweighted versions is known to be different in some classes of graphs. Trying to better understand the gap between the two versions of the problem, in the present paper we prove two complexity results. First, we extend NP-hardness of the weighted version in a certain class to the unweighted case. Second, we strengthen polynomial-time solvability of the unweighted version in the class of P2+P3-free graphs to the weighted case. This result is tight in the sense that both versions are NP-hard in the class of P3+P3-free graphs, i.e. P3+P3 is a minimal graph forbidding of which produces an NP-hard case for both versions of the problem.

Independent domination versus weighted independent domination

Mosca R.;
2020

Abstract

INDEPENDENT DOMINATION is one of the rare problems for which the complexity of weighted and unweighted versions is known to be different in some classes of graphs. Trying to better understand the gap between the two versions of the problem, in the present paper we prove two complexity results. First, we extend NP-hardness of the weighted version in a certain class to the unweighted case. Second, we strengthen polynomial-time solvability of the unweighted version in the class of P2+P3-free graphs to the weighted case. This result is tight in the sense that both versions are NP-hard in the class of P3+P3-free graphs, i.e. P3+P3 is a minimal graph forbidding of which produces an NP-hard case for both versions of the problem.
File in questo prodotto:
File Dimensione Formato  
1-s2.0-S0020019020300016-main.pdf

Solo gestori archivio

Descrizione: Article
Tipologia: PDF editoriale
Dimensione 268.25 kB
Formato Adobe PDF
268.25 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11564/717083
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact