Total domination in complements of graphs containing no K4,4 Original Research Article

We show that the total domination number of a graph G whose complement, Gc, does not contain K3,3 is at most χ(Gc), except for complete graphs, and graphs belonging to a certain family which is characterized. In the case where Gc does not contain K4,4 we show that there are four exceptional families of graphs, and determine the total domination number of the graphs in each one.