Decision Tree Complexity of Graph Properties with Dimension at Most5

A graph property is a set of graphs such that if the set contains some graph G then it also contains each isomorphic copy of G (with the same vertex set). A graph property P on n ventices is said to be elusive, if every decision tree algorithm recognizing P must examine all n(n - 1)/2 pairs of ventices in the worst case. Karp conjectured that every nontrivial monotone graph property is elusive. In this paper, this conjecture is proved for some cases. Especially,it is shown that if the abstract simplicial co…