A survey of stratified domination in graphs

A graph GG 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 FF be a 2-stratified graph with one fixed blue vertex vv specified. We say that FF is rooted at vv. The FF-domination number of a graph GG is the minimum number of red vertices of GG in a red–blue coloring of the vertices of GG such that for every blue vertex vv of GG, there is a copy of FF in GG rooted at vv. In this paper, we survey recent results on the FF-domination number for various 2-stratified graphs FF.