On Thomassen's conjecture and 2-factors of claw-free graphs

首先研究了低连通线图的2-因子分支数的上界，利用最大独立数给出了这一上界。我们得到了如下结果：3-连通无爪图有一个2-因子，其中分支数至多为2a/5，其中a是最大独立数。其次，我们考虑了三次图，它是一个非常重要的图族，对于图论中的许多重要问题和定理都有着重要的意义。并且我们证明了如果邦迪猜想在三次图上成立，那么对于最小度至少为5的情况下，罗森猜想也成立。

First, we studied the upper bounds of the number of components of 2-factors of low-connected line graphs, which are given by using the maximum independence number. And we got the following result: a 3-connected claw-free graph has a 2-factor in which the number of components is at most 2a/5, where a is the maximum independence number. Next we considered cubic graphs, which is very important family of graphs for Thomassen's conjecture and many important problems and conjectures in Graph theory. And we showed that if Bondy's conjecture on cubic graphs holds, then Thomassen's conjecture holds for the case of the minimum degree at least five.