 
Summary: Linear Time Algorithms for Finding
a Dominating Set of Fixed Size
in Degenerated Graphs
Noga Alon1,
and Shai Gutner2,
1
Schools of Mathematics and Computer Science, TelAviv University,
TelAviv, 69978, Israel
noga@math.tau.ac.il.
2
School of Computer Science, TelAviv University, TelAviv, 69978, Israel
gutner@tau.ac.il.
Abstract. There is substantial literature dealing with fixed parameter
algorithms for the dominating set problem on various families of graphs.
In this paper, we give a kO(dk)
n time algorithm for finding a dominat
ing set of size at most k in a ddegenerated graph with n vertices. This
proves that the dominating set problem is fixedparameter tractable for
degenerated graphs. For graphs that do not contain Kh as a topological
minor, we give an improved algorithm for the problem with running time
