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

Citing 6
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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 G"1(V,E"1), G"2(V,E"2), the Homogeneous Set Sandwich Problem asks whether there exists a sandwich graph G"S(V,E"S), E"1@?E"S@?E"2, which has a homogeneous set. Recently, Tang et al. [Inform. Process. Lett. 77 (2001) 17-22] proposed an interesting O(@?"1@?n^2) algorithm for this problem, which has been considered its most efficient algorithm since. We show the incorrectness of their algorithm by presenting three counterexamples.