Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A diamond is a graph obtained by removing an edge from a complete graph on four vertices. A graph is diamond-free if it does not contain an induced diamond. The Diamond-free Edge Deletion problem asks to find whether there exist at most k edges in the input graph whose deletion results in a diamond-free graph. The problem was proved to be NP-complete and a polynomial kernel of O(k^4) vertices was found by Fellows et. al. (Discrete Optimization, 2011). #R##N##R##N#,  give an improved kernel of O(k^3) vertices for Diamond-free Edge Deletion.  give an alternative proof of the NP-completeness of the problem and observe that it cannot be solved in time 2^{o(k)} * n^{O(1)}, unless the Exponential Time Hypothesis fails.
['R. B. Sandeep', 'Naveen Sivadasan']
I am writing a research paper on a idea Parameterized lower bound and improved kernel for Diamond-free Edge Deletion
[{"from": "human", "value": "I am writing a research paper on a idea Parameterized lower bound and improved kernel for Diamond-free Edge Deletion"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A diamond is a graph obtained by removing an edge from a complete graph on four vertices. A graph is diamond-free if it does not contain an induced diamond. The Diamond-free Edge Deletion problem asks to find whether there exist at most k edges in the input graph whose deletion results in a diamond-free graph. The problem was proved to be NP-complete and a polynomial kernel of O(k^4) vertices was found by Fellows et. al. (Discrete Optimization, 2011). #R##N##R##N#,  give an improved kernel of O(k^3) vertices for Diamond-free Edge Deletion.  give an alternative proof of the NP-completeness of the problem and observe that it cannot be solved in time 2^{o(k)} * n^{O(1)}, unless the Exponential Time Hypothesis fails."}]