Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  investigate the parameterized complexity of generalisations and variations#R##N#of the dominating set problem on classes of graphs that are nowhere dense.  In#R##N#particular,  show that the distance-$d$ dominating-set problem, also known#R##N#as the $(k,d)$-centres problem, is fixed-parameter tractable on any class that#R##N#is nowhere dense and closed under induced subgraphs.  This generalises known#R##N#results about the dominating set problem on $H$-minor free classes, classes#R##N#with locally excluded minors and classes of graphs of bounded expansion.  A#R##N#key feature of our proof is that it is based simply on the fact that these#R##N#graph classes are uniformly quasi-wide, and does not rely on a structural#R##N#decomposition.  Our result also establishes that the distance-$d$#R##N#dominating-set problem is FPT on classes of bounded expansion, ansring a#R##N#question of Ne{\v s}et{\v r}il and Ossona de Mendez.
['Anuj Dawar', 'Stephan Kreutzer']
I am writing a research paper on a idea Domination Problems in Nowhere-Dense Classes
[{"from": "human", "value": "I am writing a research paper on a idea Domination Problems in Nowhere-Dense Classes"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  investigate the parameterized complexity of generalisations and variations#R##N#of the dominating set problem on classes of graphs that are nowhere dense.  In#R##N#particular,  show that the distance-$d$ dominating-set problem, also known#R##N#as the $(k,d)$-centres problem, is fixed-parameter tractable on any class that#R##N#is nowhere dense and closed under induced subgraphs.  This generalises known#R##N#results about the dominating set problem on $H$-minor free classes, classes#R##N#with locally excluded minors and classes of graphs of bounded expansion.  A#R##N#key feature of our proof is that it is based simply on the fact that these#R##N#graph classes are uniformly quasi-wide, and does not rely on a structural#R##N#decomposition.  Our result also establishes that the distance-$d$#R##N#dominating-set problem is FPT on classes of bounded expansion, ansring a#R##N#question of Ne{\\v s}et{\\v r}il and Ossona de Mendez."}]