Evasiveness of subgraph containment and related properties

Amit Chakrabarti, Subhash Khot, Yaoyun Shi

Research output: Contribution to journalArticle

Abstract

We prove new results on evasiveness of monotone graph properties by extending the techniques of Kahn, Saks, and Sturtevant [Combinatorica, 4 (1984), pp. 297-306]. For the property of containing a subgraph isomorphic to a fixed graph, and a fairly large class of related n-vertex graph properties, we show evasiveness for an arithmetic progression of values of n. This implies a 1/2n2 - O(n) lower bound on the decision tree complexity of these properties. We prove that properties that are preserved under taking graph minors are evasive for all sufficiently large n. This greatly generalizes a theorem due to Best, van Emde Boas, and Lenstra [A Sharpened Version of the Aanderaa-Rosenberg Conjecture, Report ZW 30/74, Mathematisch Centrum, Amsterdam, The Netherlands, 1974] which states that planarity is evasive. We prove a similar result for bipartite subgraph containment.

Original languageEnglish (US)
Pages (from-to)866-875
Number of pages10
JournalSIAM Journal on Computing
Volume31
Issue number3
DOIs
StatePublished - 2002

Fingerprint

Decision trees
Subgraph
Graph in graph theory
Graph Minors
Planarity
Arithmetic sequence
Decision tree
Monotone
Isomorphic
Lower bound
Imply
Generalise
Vertex of a graph
Theorem

Keywords

  • Decision tree complexity
  • Evasiveness
  • Graph property testing
  • Monotone graph properties
  • Topological method

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics
  • Theoretical Computer Science

Cite this

Evasiveness of subgraph containment and related properties. / Chakrabarti, Amit; Khot, Subhash; Shi, Yaoyun.

In: SIAM Journal on Computing, Vol. 31, No. 3, 2002, p. 866-875.

Research output: Contribution to journalArticle

Chakrabarti, Amit ; Khot, Subhash ; Shi, Yaoyun. / Evasiveness of subgraph containment and related properties. In: SIAM Journal on Computing. 2002 ; Vol. 31, No. 3. pp. 866-875.
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