Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Quasi-random graphs can be informally described as graphs whose edge distribution closely resembles that of a truly random graph of the same edge density. Recently, Shapira and Yuster proved the following result on quasi-randomness of graphs. Let k ≥ 2 be a fixed integer, α1,…,αk be positive reals satisfying  \documentclass{article}\usepackage{mathrsfs}\usepackage{amsmath, amssymb}\pagestyle{empty}\begin{document} \begin{align*}\sum_{i} \alpha_i = 1\end{align*} \end{document}  and (α1,…,αk)≠(1/k,…,1/k), and G be a graph on n vertices. If for every partition of the vertices of G into sets V 1,…,V k of size α1n,…,αkn, the number of complete graphs on k vertices which have exactly one vertex in each of these sets is similar to what  would expect in a random graph, then the graph is quasi-random. Hover, the method of quasi-random hypergraphs they used did not provide enough information to resolve the case (1/k,…,1/k) for graphs. In their work, Shapira and Yuster asked whether this case also forces the graph to be quasi-random. Janson also posed the same question in his study of quasi-randomness under the framework of graph limits. ,  positively ansr their question. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011, © 2012 Wiley Periodicals, Inc.#R##N##R##N#(Supported by Samsung Scholarship.)
['H. Z. Huang', 'Choongbum Lee']
I am writing a research paper on a idea Quasi-randomness of graph balanced cut properties
[{"from": "human", "value": "I am writing a research paper on a idea Quasi-randomness of graph balanced cut properties"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Quasi-random graphs can be informally described as graphs whose edge distribution closely resembles that of a truly random graph of the same edge density. Recently, Shapira and Yuster proved the following result on quasi-randomness of graphs. Let k \u2265 2 be a fixed integer, \u03b11,\u2026,\u03b1k be positive reals satisfying  \\documentclass{article}\\usepackage{mathrsfs}\\usepackage{amsmath, amssymb}\\pagestyle{empty}\\begin{document} \\begin{align*}\\sum_{i} \\alpha_i = 1\\end{align*} \\end{document}  and (\u03b11,\u2026,\u03b1k)\u2260(1/k,\u2026,1/k), and G be a graph on n vertices. If for every partition of the vertices of G into sets V 1,\u2026,V k of size \u03b11n,\u2026,\u03b1kn, the number of complete graphs on k vertices which have exactly one vertex in each of these sets is similar to what  would expect in a random graph, then the graph is quasi-random. Hover, the method of quasi-random hypergraphs they used did not provide enough information to resolve the case (1/k,\u2026,1/k) for graphs. In their work, Shapira and Yuster asked whether this case also forces the graph to be quasi-random. Janson also posed the same question in his study of quasi-randomness under the framework of graph limits. ,  positively ansr their question. \u00a9 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011, \u00a9 2012 Wiley Periodicals, Inc.#R##N##R##N#(Supported by Samsung Scholarship.)"}]