Homomorphically full graphs (Q1917297)

As the title of this paper shows the two authors deal with homomorphically full graphs. After having given the precise definition of the concept of a homomorphically full graph and the proof of two very interesting properties of homomorphically full graphs the two authors succeed in proving the main result of this paper saying the equivalence of six different characterizations of homomorphically full graphs. It is remarkable that their proof of this main result implies polynomial-time recognition algorithms for homomorphically full graphs. R. Brewster and G. MacGillivray conclude their paper by giving a lot of interesting properties and a very long list of references. It should also be mentioned that the two authors show the relationship between homomorphically full graphs and cores and rigid graphs such that the reader is able to understand the new theory.