Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A graph   $G$   is called   \textit   {  $k$  -degenerate} if the minimum degree    $\delta (H)\le k$   for each induced   subgraph  $H$   of   $G$  .     The total generalised colourings considered     in this paper are colourings of the vertices and of the edges     of graphs satisfying the following conditions:   \\    $\bullet$   each set of vertices of the graph which receive the same colour     induces an   $m$  -degenerate graph,   \\    $\bullet$   each set of edges of the graph which receive the same colour induces an     $n$  -degenerate graph, and   \\    $\bullet$   incident elements receive different colours.   \\    Bounds for the least number of colours with which this can be done     for all   $k$  -degenerate graphs are obtained.
['Izak Broere', 'Gabriel Semanišin']
I am writing a research paper on a idea Some bounds on the generalised total chromatic number of degenerate graphs
[{"from": "human", "value": "I am writing a research paper on a idea Some bounds on the generalised total chromatic number of degenerate graphs"}, {"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   $G$   is called   \\textit   {  $k$  -degenerate} if the minimum degree    $\\delta (H)\\le k$   for each induced   subgraph  $H$   of   $G$  .     The total generalised colourings considered     in this paper are colourings of the vertices and of the edges     of graphs satisfying the following conditions:   \\\\    $\\bullet$   each set of vertices of the graph which receive the same colour     induces an   $m$  -degenerate graph,   \\\\    $\\bullet$   each set of edges of the graph which receive the same colour induces an     $n$  -degenerate graph, and   \\\\    $\\bullet$   incident elements receive different colours.   \\\\    Bounds for the least number of colours with which this can be done     for all   $k$  -degenerate graphs are obtained."}]