The chain graph sandwich problem

Simone Dantas; Celina M.H. de Figueiredo; Martin Charles Golumbic; Sulamita Klein; Frédéric Maffray

doi:10.1007/s10479-010-0792-0

The chain graph sandwich problem

Simone Dantas
, Celina M.H. de Figueiredo
, Martin Charles Golumbic
, Sulamita Klein
, Frédéric Maffray

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

The chain graph sandwich problem asks: Given a vertex set V, a mandatory edge set E¹, and a larger edge set E², is there a graph G=(V,E) such that E¹⊆E⊆E² with G being a chain graph (i. e., a 2K₂-free bipartite graph)? We prove that the chain graph sandwich problem is NP-complete. This result stands in contrast to (1) the case where E¹ is a connected graph, which has a linear-time solution, (2) the threshold graph sandwich problem, which has a linear-time solution, and (3) the chain probe graph problem, which has a polynomial-time solution.

Original language	English
Pages (from-to)	133-139
Number of pages	7
Journal	Annals of Operations Research
Volume	188
Issue number	1
DOIs	https://doi.org/10.1007/s10479-010-0792-0
State	Published - Aug 2011

Bibliographical note

Funding Information:
This research was partially supported by CNPq, CAPES (Brazil)/COFECUB (France), FAPERJ.

ASJC Scopus subject areas

General Decision Sciences
Management Science and Operations Research

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10.1007/s10479-010-0792-0

Cite this

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title = "The chain graph sandwich problem",

abstract = "The chain graph sandwich problem asks: Given a vertex set V, a mandatory edge set E1, and a larger edge set E2, is there a graph G=(V,E) such that E1⊆E⊆E2 with G being a chain graph (i. e., a 2K2-free bipartite graph)? We prove that the chain graph sandwich problem is NP-complete. This result stands in contrast to (1) the case where E1 is a connected graph, which has a linear-time solution, (2) the threshold graph sandwich problem, which has a linear-time solution, and (3) the chain probe graph problem, which has a polynomial-time solution.",

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AU - Dantas, Simone

AU - de Figueiredo, Celina M.H.

AU - Golumbic, Martin Charles

AU - Klein, Sulamita

AU - Maffray, Frédéric

N1 - Funding Information: This research was partially supported by CNPq, CAPES (Brazil)/COFECUB (France), FAPERJ.

PY - 2011/8

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The chain graph sandwich problem

Abstract

Bibliographical note

ASJC Scopus subject areas

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