正则图的若干问题的研究

图论中的一些问题, 如双圈覆盖猜想、Tutte的5-流猜想，Sheehan 猜想，都归结为研究正则图，特别是3-正则或4-正则图。在此项目中，我们将研究正则图的特殊的2-因子与划分的存在性问题，及团横贯数。此项研究与图的着色，划分，控制，及因子理论的研究有紧密关系。我们期望解决若干相关的公开问题与猜想。

A number of problems in grpah theory, such as cycle doucle cover conjectue, Tutte's 5-flow conjecture, Sheehan conjecture, can be reduced to study the correponding problems on the regular graphs, particulariy, the cubic or 4-regular graphas. We investigate the existence of 2-factor and partition with special properties and the clique transversal number of reguar graphs. This study has a close connection to that of colorings, partitions, dominations and facors in grpah theory. We aim to solve several open problems and related conjectures.