Ramsey-Turan若干问题高级研讨班

Ramsey-Turan问题是极值图论中较为困难的问题，同时也是目前研究的热点问题。在此类问题中，Ramsey-Turan密度的研究受到极大关注。Erdos, Hajnal, Simonovits, Sos和Szemeredi[Combinatorica, 1983]提出如下问题：确定三角形对p阶完全图的二色Ramsey-Turan密度。另外，Kim, Kim和Liu[SIAM J. Discrete Math, 2019]提出更加精确的猜想。项目申请人和研究人员长期从事图论领域研究工作，取得了一系列的研究成果。本项目拟搭建Ramsey-Turan若干问题研究的学术交流平台。我们将邀请国内外知名图论学者，包括国内外高水平、优秀的中青年图论学者，并组建科研小组，就二色Ramsey-Turan密度等相关极值问题展开讨论，争取在Ramsey-Turan问题上取得突破性进展。

Ramsey-turan problem is a class difficult problem in extremum graph theory, and it is also one of the hot issues in the current research. Among such problems, the study of Ramsey-Turan density has attracted great attention. Erdos, Hajnal, Simonovits, Sos and Szemeredi [Combinatorica, 1983] presented the following problem: Determining the two color Ramsey-Turan density of a triangle versus a complete graph of order P. Moreover, Kim, Kim和Liu[SIAM J. Discrete Math, 2019] proposed a more subtle conjecture on the two color Ramsey-Turan density. We have been engaged in the work of graph theory for a long time and obtained a series of achievements. This project intends to build an academic exchange platform for several Ramsey-Turan problems. We will invite famous scholars at home and abroad, including high-level, excellent young and middle-aged scholars of graph theory, and we will establish a scientific research group in order to discuss the two-color Ramsey-Turan density and related problems. We aim to make a great breakthrough and promote the development of Ramsey-Turan problems through this project.