无爪图的哈密尔顿性和2-因子问题

无爪图的研究一直是许多图论研究者感兴趣的课题之一，这方面研究众多，出现了许多经典的结论。本项目主要研究图论中无爪图的哈密尔顿问题和无爪图的2-因子问题。包括连通，N^m-局部连通无爪图哈密尔顿圈的存在问题和边在小圈上的无爪图的2-因子存在问题。这些问题在研究方法上将有所改进。 我们的结论将有望加强和推广已知结果。

The research of claw-free graphs has been one of the topics of many graph theory reseachers interested in. Reseach in this field is multitudinous and there are many classical results. In this project， we systematically study some problems about the Hamiltonicity and 2-factor of claw-free graphs , including the existence of Hamiltonian cycle of claw-free graphs and the existence of 2-factors of claw-free graphs whose edges in small cycle. These problems will be improved in reseach methods. Our results are expected to strengthen the known results.