Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the complexity of a group of distance-constrained graph labeling problems when parameterized by the neighborhood diversity ($nd$), which is a natural graph parameter beten vertex cover and clique width. Neighborhood diversity has been used to generalize and speed up \sf{FPT} algorithms previously parameterized by vertex cover, as is also demonstrated by our paper. #R##N# show that the {\sc Uniform Channel Assignment} problem is fixed parameter tractable when parameterized by $nd$ and the largest ight and that every {\sc $L(p_1, p_2,\dots, p_k)$-labeling} problem is \sf{FPT} when parameterized by $nd$, maximum $p_i$ and $k$. #R##N#These results furthermore yield an \sf{FPT} algorithms for {\sc $L(p_1, p_2,\dots, p_k)$-labeling} and {\sc Channel Assignment} problems when parameterized by vertex cover size, ansring an open question of Fiala et al.: {\emph Parameterized complexity of coloring problems: Treewidth versus vertex cover}, generalizing their results beyond $L(2,1)$-labeling, and tightening the complexity gap to clique width, where the problems are already hard for constant clique width.
['Jirí Fiala', 'Tomáš Gavenčiak', 'Dušan Knop', 'Martin Koutecký', 'Jan Kratochvíl']
I am writing a research paper on a idea Distance constrained labeling on graphs with bounded neighborhood diversity.
[{"from": "human", "value": "I am writing a research paper on a idea Distance constrained labeling on graphs with bounded neighborhood diversity."}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the complexity of a group of distance-constrained graph labeling problems when parameterized by the neighborhood diversity ($nd$), which is a natural graph parameter beten vertex cover and clique width. Neighborhood diversity has been used to generalize and speed up \\sf{FPT} algorithms previously parameterized by vertex cover, as is also demonstrated by our paper. #R##N# show that the {\\sc Uniform Channel Assignment} problem is fixed parameter tractable when parameterized by $nd$ and the largest ight and that every {\\sc $L(p_1, p_2,\\dots, p_k)$-labeling} problem is \\sf{FPT} when parameterized by $nd$, maximum $p_i$ and $k$. #R##N#These results furthermore yield an \\sf{FPT} algorithms for {\\sc $L(p_1, p_2,\\dots, p_k)$-labeling} and {\\sc Channel Assignment} problems when parameterized by vertex cover size, ansring an open question of Fiala et al.: {\\emph Parameterized complexity of coloring problems: Treewidth versus vertex cover}, generalizing their results beyond $L(2,1)$-labeling, and tightening the complexity gap to clique width, where the problems are already hard for constant clique width."}]