Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In the Block Graph Deletion problem,  are given a graph G on n vertices and a positive integer k, and the objective is to check whether it is possible to delete at most k vertices from G to make it a block graph, i.e., a graph in which each block is a clique. ,  obtain a kernel with O(k^{6}) vertices for the Block Graph Deletion problem. This is a first step to investigate polynomial kernels for deletion problems into non-trivial classes of graphs of bounded rank-width, but unbounded tree-width. Our result also implies that Chordal Vertex Deletion admits a polynomial-size kernel on diamond-free graphs. For the kernelization and its analysis,  introduce the notion of 'complete degree' of a vertex.  believe that the underlying idea can be potentially applied to other problems.  also prove that the Block Graph Deletion problem can be solved in time 10^{k} * n^{O(1)}.
['Eun Jung Kim', 'O-joung Kwon']
I am writing a research paper on a idea A polynomial kernel for Block Graph Deletion
[{"from": "human", "value": "I am writing a research paper on a idea A polynomial kernel for Block Graph Deletion"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In the Block Graph Deletion problem,  are given a graph G on n vertices and a positive integer k, and the objective is to check whether it is possible to delete at most k vertices from G to make it a block graph, i.e., a graph in which each block is a clique. ,  obtain a kernel with O(k^{6}) vertices for the Block Graph Deletion problem. This is a first step to investigate polynomial kernels for deletion problems into non-trivial classes of graphs of bounded rank-width, but unbounded tree-width. Our result also implies that Chordal Vertex Deletion admits a polynomial-size kernel on diamond-free graphs. For the kernelization and its analysis,  introduce the notion of 'complete degree' of a vertex.  believe that the underlying idea can be potentially applied to other problems.  also prove that the Block Graph Deletion problem can be solved in time 10^{k} * n^{O(1)}."}]