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An analogue of the Erdős–Gallai theorem for random graphs
European Journal of Combinatorics ( IF 1.0 ) Pub Date : 2020-08-25 , DOI: 10.1016/j.ejc.2020.103200 József Balogh , Andrzej Dudek , Lina Li
中文翻译:
随机图的Erdős-Gallai定理的类似物
更新日期:2020-08-25
European Journal of Combinatorics ( IF 1.0 ) Pub Date : 2020-08-25 , DOI: 10.1016/j.ejc.2020.103200 József Balogh , Andrzej Dudek , Lina Li
Recently, variants of many classical extremal theorems have been proved in the random environment. We, complementing existing results, extend the Erdős–Gallai Theorem in random graphs. In particular, we determine, up to a constant factor, the maximum number of edges in a -free subgraph of , practically for all values of and . Our work is also motivated by the recent progress on the size-Ramsey number of paths.
中文翻译:
随机图的Erdős-Gallai定理的类似物
最近,在随机环境中已经证明了许多经典极值定理的变体。我们对现有结果进行补充,在随机图中扩展了Erdős-Gallai定理。尤其是,我们确定一个恒定因子,即的免费子图 ,实际上适用于 和 。我们的工作也受到最近在规模-拉姆西路径上取得进展的推动。