Basic Problems in Extremal Graph Theory

极值问题是经典图论的核心。虽然该地区已经写了数百篇论文，但一些基本问题仍然没有解决。令我非常惊讶的是，不久前一个臭名昭著的问题得到了回答：每个有n个顶点且Bn2=4c+m条边的K4-Free图包含m个边不相交的三角形。尽管如此，这个漂亮的结果并不是这个话题的最后结论：我希望Jan在继续讨论一些相关问题之前，可以大大改进这个结果。

Extremal problems are at the heart of classical graph theory. Although hundreds of papers have been written in the area, some of the basic problems are still unsolved. I was very surprised that a short while ago one of the notorious questions was answered: every K4-freegraph with n vertices and bn2=4c + m edges contains m edge-disjoint triangles. Still, this beautiful result is not the last word on the topic: I hope that Jan can improve this result considerably before going on to some related problems.