斯坦纳树填装数猜想与图的树连通度

Nash-Williams-Tutte定理既是结构图论中的经典结果，又是生成树填装问题研究中的重要工具。作为生成树的自然推广，斯坦纳树在大规模集成电路设计和网络科学方面有着重要应用。Kriesell在2013年提出的关于斯坦纳树填装问题的猜想是Nash-Williams-Tutte定理的推广。在这个猜想的带动下，学者们在近10多年里取得了一些重要进展，同时也获得了一些方法和技巧。与此同时，West和Wu在2012年提出了关于S-连通子的猜想。目前，这两个猜想仍然没有解决。树连通度是经典连通度的推广，是斯坦纳树填装问题方面的另一个图参数。. 本项目运用经典结构图论和极值图论诸多研究工具和代数方法研究Kriesell猜想，West-Wu猜想和树连通度。

The Nash-Williams-Tutte Theorem about spanning-tree packing problem is both a classical result and an important tool in structural graph theory. Steiner tree is a natural generalization of spanning tree and is popularly used in the physical design of VLSI circuits and network science. In 2003, Kriesell proposed a conjecture about Steiner tree packing problem, which can be seen as a generalization of the Nash-Williams-Tutte Theorem. Motivated by this conjecture, researchers have made important progress and obtained some technical methods in recent ten years. Also, West and Wu in 2012 proposed a new conjecture about S-connector. These conjectures are still open now. Tree-connectivity is a generalization of classical connectivity, which is another structural parameter of Steiner tree packing problem.. In this project, we are devoted to study Kriesell conjecture, West-Wu conjecture and tree-connectivity by classical tools in structural graph theory, extremal graph theory and algebra theory.