In this paper we solve two problems of Esperet, Kang and Thomasse as well as Li concerning (i) induced bipartite subgraphs in triangle-free graphs and (ii) van der Waerden numbers. Each time random greedy algorithms allow us to go beyond the Lovasz Local Lemma or alteration method used in previous work, illustrating the power of the algorithmic approach to the probabilistic method.

翻译：在本文中,我们解决了Esperet、Kang和Thomasse以及Li的两个问题,即(一) 三角无边图表中诱导的两边子子集和(二) 范德华登数字。 每次随机贪婪算法允许我们超越Lovasz Lemma(Lovasz Lemma)或先前工作中使用的改变方法,这说明了算法方法对概率方法的力量。