Complexity of 2-rainbow total domination problemKraner Šumenjak, Tadeja (Avtor) Tepeh, Aleksandra (Avtor) dominationrainbow dominationrooted productNP-completeIn 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.20242024-08-26 10:51:41Neznano20226UDK: 519.17ISSN pri članku: 0126-6705DOI: 10.1007/s40840-024-01747-8COBISS_ID: 204512515sl