Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the next random process for generating a maximal H-free graph: Given a xed graph H and an integer n, start by taking a uniformly random permutation of the edges of the complete n-vertex graph Kn. Then, traverse the edges of Kn according to the order imposed by the permutation and add each traversed edge to an (initially empty) evolving n-vertex graph - unless its addition creates a copy of H. The result of this process is a maximal H-free graph Mn(H). Our main result is a new lor bound on the expected number of edges in Mn(H), for H that is regular, strictly 2-balanced. As a corollary,  obtain new lor bounds for Tur an numbers of complete, balanced bipartite graphs. Namely, for xed r 5,  show
['Guy Wolfovitz']
I am writing a research paper on a idea Lower Bounds for the Size of Random Maximal H-Free Graphs
[{"from": "human", "value": "I am writing a research paper on a idea Lower Bounds for the Size of Random Maximal H-Free Graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the next random process for generating a maximal H-free graph: Given a xed graph H and an integer n, start by taking a uniformly random permutation of the edges of the complete n-vertex graph Kn. Then, traverse the edges of Kn according to the order imposed by the permutation and add each traversed edge to an (initially empty) evolving n-vertex graph - unless its addition creates a copy of H. The result of this process is a maximal H-free graph Mn(H). Our main result is a new lor bound on the expected number of edges in Mn(H), for H that is regular, strictly 2-balanced. As a corollary,  obtain new lor bounds for Tur an numbers of complete, balanced bipartite graphs. Namely, for xed r 5,  show"}]