| Title: | A note on domination and independence-domination numbers of graphs |
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| Authors: | ID Milanič, Martin (Author) |
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| Files: |  RAZ_Milanic_Martin_i2013.pdf (300,57 KB)
MD5: 653E076C3F1DE2F04B4C14DB3DD5D0BA
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| Language: | English |
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| Work type: | Unknown |
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| Typology: | 1.08 - Published Scientific Conference Contribution |
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| Organization: | ZUP - University of Primorska Press
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| 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 ▫$\gamma^i < \gamma$▫. |
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| Keywords: | Vizing's conjecture, domination number, independence-domination number, weakly chordal graph, NP-completeness, hereditary graph class, IDD-perfect graph |
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| Year of publishing: | 2013 |
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| Number of pages: | str. 89-97 |
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| Numbering: | Vol. 6, no. 1 |
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| PID: | 20.500.12556/RUP-2624  |
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| UDC: | 519.17 |
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| ISSN on article: | 1855-3966 |
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| COBISS.SI-ID: | 1024423764 |
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| Publication date in RUP: | 15.10.2013 |
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| Views: | 3541 |
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| Downloads: | 131 |
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| Metadata: |    |
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