Martin Milanič (Author)

Abstract

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 ▫$\gamma^i < \gamma$▫.

Keywords

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

Data

Language: English
Year of publishing:
Typology: 1.08 - Published Scientific Conference Contribution
Organization: UP - University of Primorska
UDC: 519.17
COBISS: 1024423764 Link will open in a new window
ISSN: 1855-3966
Views: 2926
Downloads: 128
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Other data

Secondary language: English
Type (COBISS): Not categorized
Pages: str. 89-97
Volume: ǂVol. ǂ6
Issue: ǂno. ǂ1
Chronology: 2013
ID: 14092545
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