Martin Milanič (Avtor)

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:
Tipologija: 1.08 - Objavljeni znanstveni prispevek na konferenci
Organizacija: UP - Univerza na Primorskem
UDK: 519.17
COBISS: 1024423764 Povezava se bo odprla v novem oknu
ISSN: 1855-3966
Št. ogledov: 2926
Št. prenosov: 128
Ocena: 0 (0 glasov)
Metapodatki: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

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
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