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The graph sandwich problem for 1-join composition is NP-complete

de Figueiredo, CMH, Klein, S and Vuskovic, K (2002) The graph sandwich problem for 1-join composition is NP-complete. Discrete Applied Mathematics, 121 (1-3). 73 - 82 . ISSN 0166-218X

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Abstract

A graph is a 1-join composition if its vertex set can be partitioned into four nonempty sets and SR such that: every vertex of AL is adjacent to every vertex of AR; no vertex of SL is adjacent to vertex of AR∪SR; no vertex of SR is adjacent to a vertex of AL∪SL. The graph sandwich problem for 1-join composition is defined as follows: Given a vertex set V, a forced edge set E1, and a forbidden edge set E3, is there a graph G=(V,E) such that E1⊆E and E∩E3=∅, which is a 1-join composition graph? We prove that the graph sandwich problem for 1-join composition is NP-complete. This result stands in contrast to the case where SL=∅ (SR=∅), namely, the graph sandwich problem for homogeneous set, which has a polynomial-time solution.

Item Type: Article
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 22 Jun 2012 10:17
Last Modified: 08 Feb 2013 17:39
Published Version: http://dx.doi.org/10.1016/S0166-218X(01)00246-3
Status: Published
Publisher: Elsevier for North-Holland Publishing
Identification Number: 10.1016/S0166-218X(01)00246-3
URI: http://eprints.whiterose.ac.uk/id/eprint/74359

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