We discuss sampling constants for dominating sets in Bergman spaces. Our method is based on a Remez-type inequality by Andrievskii and Ruscheweyh. also comment extensions of the to other spaces such as Fock Paley-Wiener

For a graph G that models a facility, various detection devices can be placed at the vertices so as to identify the location of an intruder such as a thief or saboteur. Here we introduce the open neighborhood locating-dominating set problem. We seek a minimum cardinality vertex set S with the property that for each vertex v its open neighborhood N(v) has a unique non-empty intersection with S. ...

It is known that the treewidth of a planar graph with a dominating set of size d is O( √ d) and this fact is used as the basis for several fixed parameter algorithms on planar graphs. An interesting question motivating our study is if similar bounds can be obtained for larger minor closed graph families. We say that a graph family F has the domination-treewidth property if there is some functio...