Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A remarkable result of Friedman and Pippenger gives a sufficient condition on the expansion properties of a graph to contain all small trees with bounded maximum degree. Haxell shod that under slightly stronger assumptions on the expansion rate, their technique allows one to find arbitrarily large trees with bounded maximum degree. Using a slightly aker version of Haxell's result  prove that a certain family of expanding graphs, which includes very sparse random graphs and regular graphs with large enough spectral gap, contains all almost spanning bounded degree trees. This improves two recent tree-embedding results of Alon, Krivelevich and Sudakov.
['József Balogh', 'Béla Csaba', 'Martin Pei', 'Wojciech Samotij']
I am writing a research paper on a idea Large bounded degree trees in expanding graphs
[{"from": "human", "value": "I am writing a research paper on a idea Large bounded degree trees in expanding graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A remarkable result of Friedman and Pippenger gives a sufficient condition on the expansion properties of a graph to contain all small trees with bounded maximum degree. Haxell shod that under slightly stronger assumptions on the expansion rate, their technique allows one to find arbitrarily large trees with bounded maximum degree. Using a slightly aker version of Haxell's result  prove that a certain family of expanding graphs, which includes very sparse random graphs and regular graphs with large enough spectral gap, contains all almost spanning bounded degree trees. This improves two recent tree-embedding results of Alon, Krivelevich and Sudakov."}]