A Survey of Stratified Domination in Graphs
A graph G is 2-stratified if its vertex set is partitioned into two nonempty classes (each of which is a stratum or a color class). We color the vertices in one color class red and the other color class blue. Let F be a 2-stratified graph with one fixed blue vertex v specified. We say that F is rooted at v. The F-domination number of a graph G is the minimum number of red vertices of G in a red-blue coloring of the vertices of G such that for every blue vertex v of G, there is a copy of F in G rooted at v. In this paper, we survey recent results on the F-domination number for various 2-stratified graphs F.
Haynes, Teresa W.; Henning, Michael A.; and Zhang, Ping. 2009. A Survey of Stratified Domination in Graphs. Discrete Mathematics. Vol.309(19). 5806-5819. https://doi.org/10.1016/j.disc.2008.02.048 ISSN: 0012-365X