| Title: | Complexity of 2-rainbow total domination problem |
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| Authors: | ID Kraner Šumenjak, Tadeja (Author)
ID Tepeh, Aleksandra (Author) |
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| Files: |  PDF - Presentation file, download (391,20 KB)
MD5: 22D44F33D85AFC2D4B25C054EC78E837
 URL - Source URL, visit https://link.springer.com/article/10.1007/s40840-024-01747-8
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | In this paper,we extend the findings of recent studies on $k$-rainbow total domination by placing our focus on its computational complexity aspects. We show that the problem of determining whether a graph has a $2$-rainbow total dominating function of a given weight is NP-complete. This complexity result holds even when restricted to planar graphs. Along the way tight bounds for the $k$-rainbow total domination number of rooted product graphs are established. In addition, we obtain the closed formula for the $k$-rainbow total domination number of the corona product $G ∗ H$, provided that $H$ has enough vertices. |
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| Keywords: | domination, rainbow domination, rooted product, NP-complete |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.09.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | 12 str. |
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| Numbering: | Vol. 47, iss. 5, article no. 155 |
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| PID: | 20.500.12556/DiRROS-20226  |
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| UDC: | 519.17 |
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| ISSN on article: | 0126-6705 |
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| DOI: | 10.1007/s40840-024-01747-8 |
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| COBISS.SI-ID: | 204512515 |
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| Note: |
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| Publication date in DiRROS: | 26.08.2024 |
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| Views: | 796 |
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| Downloads: | 438 |
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| Metadata: |    |
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