Note on the homogeneous set sandwich problem

  • Authors:

  • Celina M. H. de Figueiredo;Vinícius G. P. de Sá

  • Affiliations:

  • Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21945-970 Rio de Janeiro, RJ, Brazil;Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21945-970 Rio de Janeiro, RJ, Brazil

  • Venue:
  • Information Processing Letters
  • Year:
  • 2005

Quantified Score

Hi-index 0.89

Visualization

Abstract

A homogeneous set is a non-trivial module of a graph, i.e., a non-unitary, proper subset H of a graph's vertices such that all vertices in H have the same neighbors outside H. Given two graphs G1(V, E1), G2(V, E2), the Homogeneous Set Sandwich Problem asks whether there exists a sandwich graph GS(V, ES), E1 ⊆ ES ⊆ E2, which has a homogeneous set. Recently, Tang et al. [Inform. Process. Lett. 77 (2001) 17-22] proposed an interesting O(Δ1 ċ n2) algorithm for this problem, which has been considered its most efficient algorithm since. We show the incorrectness of their algorithm by presenting three counterexamples.