  We consider the so-called coupon-coloring of the vertices of a graph where
every color appears in every open neighborhood, and our aim is to determine the
maximal number of colors in such colorings. In other words, every color class
must be a total dominating set in the graph and we study the total domatic
number of the graph. We determine this parameter in every maximal outerplanar
graph, and show that every Hamiltonian maximal planar graph has domatic number
at least two, partially answering a conjecture of Goddard and Henning.
