ǂA ǂnote on domination and independence-domination numbers of graphs

Povzetek

Vizing's conjecture is true for graphs ▫$G$▫ satisfying ▫$\gamma^i(G) = \gamma(G)$▫, where ▫$\gamma(G)$▫ is the domination number of a graph ▫$G$▫ and ▫$\gamma^i(G)$▫ is the independence-domination number of ▫$G$▫, that is, the maximum, over all independent sets ▫$I$▫ in ▫$G$▫, of the minimum number of vertices needed to dominate ▫$I$▫. The equality ▫$\gamma^i(G) = \gamma(G)$▫ is known to hold for all chordal graphs and for chordless cycles of length ▫$0 \pmod{3}$▫. We prove some results related to graphs for which the above equality holds. More specifically, we show that the problems of determining whether ▫$\gamma^i(G) = \gamma(G) = 2$▫ and of verifying whether ▫$\gamma^i(G) \ge 2$▫ are NP-complete, even if ▫$G$▫ is weakly chordal. We also initiate the study of the equality ▫$\gamma^i = \gamma$▫ in the context of hereditary graph classes and exhibit two infinite families of graphs for which ▫$\gamma^i < \gamma$▫.

Ključne besede

Vizing's conjecture;domination number;independence-domination number;weakly chordal graph;NP-completeness;hereditary graph class;IDD-perfect graph;

Podatki

Jezik:	Angleški jezik
Leto izida:	2013
Tipologija:	1.08 - Objavljeni znanstveni prispevek na konferenci
Organizacija:	UP - Univerza na Primorskem
UDK:	519.17
COBISS:	1024423764
ISSN:	1855-3966
Št. ogledov:	2926
Št. prenosov:	128
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
Vrsta dela (COBISS):	Delo ni kategorizirano
Strani:	str. 89-97
Letnik:	ǂVol. ǂ6
Zvezek:	ǂno. ǂ1
Čas izdaje:	2013
ID:	14092545