A Roman dominating function (RDF) on a graph $G = (V, E)$ is a labeling $f : V rightarrow {0, 1, 2}$ suchthat every vertex with label $0$ has a neighbor with label $2$. The weight of $f$ is the value $f(V) = Sigma_{vin V} f(v)$The Roman domination number, $gamma_R(G)$, of $G$ is theminimum weight of an RDF on $G$.An RDF of minimum weight is called a $gamma_R$-function.A graph G is said to be $g...

A careful exposition of Zilber’s quasiminimal excellent classes and their categoricity is given, leading to two new results: the Lω1,ω(Q)definability assumption may be dropped, and each class is determined by its model of dimension א0. Boris Zilber developed quasiminimal excellent classes in [Zil05], in order to prove that his conjectural description of complex exponentiation was categorical. T...