Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A subgraph of a graph G is called trivial if it is either a clique or an independent set. Let q(G) denote the maximum number of vertices in a trivial subgraph of G. Motivated by an open problem of Erdos and McKay  show that every graph G on n vertices for which q(G)≤ C log n contains an induced subgraph with exactly y edges, for every y beten 0 and nδ (C). Our methods enable us also to show that under much aker assumption, i.e., q(G) ≤ n-14, G still must contain an induced subgraph with exactly y edges, for every y beten 0 and $e^{\Omega} (\sqrt { \log\, n})$. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 239251, 2003
['Noga Alon', 'Michael Krivelevich', 'Benny Sudakov']
I am writing a research paper on a idea Induced subgraphs of prescribed size
[{"from": "human", "value": "I am writing a research paper on a idea Induced subgraphs of prescribed size"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A subgraph of a graph G is called trivial if it is either a clique or an independent set. Let q(G) denote the maximum number of vertices in a trivial subgraph of G. Motivated by an open problem of Erdos and McKay  show that every graph G on n vertices for which q(G)\u2264 C log n contains an induced subgraph with exactly y edges, for every y beten 0 and n\u03b4 (C). Our methods enable us also to show that under much aker assumption, i.e., q(G) \u2264 n-14, G still must contain an induced subgraph with exactly y edges, for every y beten 0 and $e^{\\Omega} (\\sqrt { \\log\\, n})$. \u00a9 2003 Wiley Periodicals, Inc. J Graph Theory 43: 239251, 2003"}]