ABSTRACT
Vizing’s conjecture, the central open problem of domination theory, concerns the domination number of Cartesian products. We investigate this conjecture in Sections 28.1 and 28.2. Then, in Section 28.3, we turn to the the fractional domination number and prove that the fractional version of Vizing’s conjecture is true. Along the way we obtain several results about the domination number for strong products. The final section treats domination of direct products.
