Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A graph is $\ell$-choosable if, for any choice of lists of $\ell$ colors for each vertex, there is a list coloring, which is a coloring where each vertex receives a color from its list.  study complexity issues of choosability of graphs when the number $k$ of colors is limited.  get results which differ surprisingly from the usual case where $k$ is implicit and which extend known results for the usual case.  also exhibit some classes of graphs (defined by structural properties of their blocks) which are choosable. Finally  show that for any $\ell\geq 3$ and any $k\geq 2\ell-2$ there is a bipartite graph which is $\ell$-choosable with $k$ colors but not with $k+1$.
['Marc Demange', 'Dominique de Werra']
I am writing a research paper on a idea Choosability with limited number of colors
[{"from": "human", "value": "I am writing a research paper on a idea Choosability with limited number of colors"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A graph is $\\ell$-choosable if, for any choice of lists of $\\ell$ colors for each vertex, there is a list coloring, which is a coloring where each vertex receives a color from its list.  study complexity issues of choosability of graphs when the number $k$ of colors is limited.  get results which differ surprisingly from the usual case where $k$ is implicit and which extend known results for the usual case.  also exhibit some classes of graphs (defined by structural properties of their blocks) which are choosable. Finally  show that for any $\\ell\\geq 3$ and any $k\\geq 2\\ell-2$ there is a bipartite graph which is $\\ell$-choosable with $k$ colors but not with $k+1$."}]