几类子树超图相关组合代数性质

Combinatcrial and algebraic properties on several classes of subtree hypergraphs

拟在子树超图这一重要的图论对象上研究与顶点可分解和shellable相关的组合代数性质.在给定树上删除一个点时,都可构造出一个保持一定的子树关系的新树.借助这一构造以及归纳法,证明了极大完全子树超图都是顶点可分解的;对于由路径诱导的任一子树超图,利用字典序构造出其独立复形的极大面上的一个shelling序,从而证明了其满足shellable性质.

In the report,the combinatorial algebra properties related to the vertex decomposability and shellabili⁃ty on subtree hypergraphs were studied.When deleting a vertex from a given tree,a new tree which preserves some subtree relations can always be constructed.Based on the construction and the mathematical induction,it was proven that all the maximal complete subtree hypergraphs are vertex decomposable.For a subtree hyper⁃graph induced by a path,the lexicographical order was used to construct a shelling order on the facet set of its in⁃dependence complex,and which prove that it can satisfied with shellability.