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.
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