20.500.12556/DiRROS-20226 Complexity of 2-rainbow total domination problem 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. domination rainbow domination rooted product NP-complete dominacija mavrična dominacija matematika true false true Angleški jezik Slovenski jezik Neznano 2024-08-26 10:51:41 2024-08-26 10:51:41 2024-08-27 03:35:32 0000-00-00 00:00:00 2024 0 0 12 str. iss. 5, article no. 155 Vol. 47 Sep. 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2024-09-01 519.17 0126-6705 10.1007/s40840-024-01747-8 204512515 s40840-024-01747-8.pdf s40840-024-01747-8.pdf 1 22D44F33D85AFC2D4B25C054EC78E837 555ef30b72c308a144f6ff4a296a2d3375df4ed7773571a6ceb373451e7c3c38 06caf417-6378-11ef-b487-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=28329 https://link.springer.com/article/10.1007/s40840-024-01747-8 1 a7a5643b-6377-11ef-b487-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=28328 Inštitut za matematiko, fiziko in mehaniko 0 0 0