Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: For graphs of bounded maximum degree,  consider acyclic t-improper colourings, that is, colourings in which each bipartite subgraph consisting of the edges beten two colour classes is acyclic, and each colour class induces a graph with maximum degree at most t.  consider the supremum, over all graphs of maximum degree at most d, of the acyclic t-improper chromatic number and provide t-improper analogues of results by Alon, McDiarmid and Reed [N. Alon, C.J.H. McDiarmid, B. Reed, Acyclic coloring of graphs, Random Structures Algorithms 2 (3) (1991) 277-288] and Fertin, Raspaud and Reed [G. Fertin, A. Raspaud, B. Reed, Star coloring of graphs, J. Graph Theory 47 (3) (2004) 163-182].
['Louigi Addario-Berry', 'Louis Esperet', 'Ross J. Kang', 'Colin McDiarmid', 'Alexandre Pinlou']
I am writing a research paper on a idea Acyclic improper colourings of graphs with bounded maximum degree
[{"from": "human", "value": "I am writing a research paper on a idea Acyclic improper colourings of graphs with bounded maximum degree"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: For graphs of bounded maximum degree,  consider acyclic t-improper colourings, that is, colourings in which each bipartite subgraph consisting of the edges beten two colour classes is acyclic, and each colour class induces a graph with maximum degree at most t.  consider the supremum, over all graphs of maximum degree at most d, of the acyclic t-improper chromatic number and provide t-improper analogues of results by Alon, McDiarmid and Reed [N. Alon, C.J.H. McDiarmid, B. Reed, Acyclic coloring of graphs, Random Structures Algorithms 2 (3) (1991) 277-288] and Fertin, Raspaud and Reed [G. Fertin, A. Raspaud, B. Reed, Star coloring of graphs, J. Graph Theory 47 (3) (2004) 163-182]."}]