I have been attempting to learn parameterized complexity on my own, and decided to go through all of the FPT race problems, and defining easy FPT algorithms for them, using concepts such as bounded search tree. I am stuck on figuring out an FPT algorithm for edge dominating set, defined as follows:
Instance: A graph $G=(V,E)$; a positive integer $k$.
Question: Is there a subset $D\subseteq E$ with $|D|\leq k$ such that for each $e\in E$, either $e\in D$ or $e$ shares an endpoint with an $e'\in D$.
I'm not looking to define anything fancy, just a simple FPT result. Any help would be great!