Lower bounds for testing forbidden induced substructures in bipartite-graph-like combinatorial objects

  • Authors:
  • Eldar Fischer;Eyal Rozenberg

  • Affiliations:
  • Department of Computer Science, Technion, Haifa, Israel;Department of Computer Science, Technion, Haifa, Israel

  • Venue:
  • APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
  • Year:
  • 2007

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Abstract

We investigate the property of k-uniform k-partite (directed) hypergraphs with colored edges of being free of a fixed family of forbidden induced substructures. We show that this property is not testable with a number of queries polynomial in 1/茂戮驴, presenting proofs for the case of two colors and k= 3, as well as the case of three colors and k= 2 (edge-colored bipartite graphs). This settles an open question from [1], implying that the polynomial testability proof for two colors and k= 2 cannot be extended to these structures.