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Journal of Computer Science and Technology

, Volume 15, Issue 5, pp 416–422 | Cite as

Decision tree complexity of graph properties with dimension at most 5

  • Gao Suixiang Email author
  • Lin Guohui 
Article

Abstract

A graph property is a set of graphs such that if the set contains some graphG then it also contains each isomorphic copy ofG (with the same vertex set). A graph propertyP onn vertices is said to be elusive, if every decision tree algorithm recognizingP must examine alln(n−1)/2, pairs of vertices 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 complex of a nontrivial monotone graph propertyP has dimension not exceeding 5, thenP is elusive.

Keywords

monotone graph property decision tree complexity elusive 

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Copyright information

© Science Press, Beijing China and Allerton Press Inc. 2000

Authors and Affiliations

  1. 1.Mathematics Department, Graduate SchoolUniversity of Science and Technology of ChinaBeijingP.R. China
  2. 2.Department of Computer ScienceUniversity of WaterlooWaterlooCanada

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