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Complexity of diagrams

Complexity of diagrams Order 10: 393, 1993. 393 © 1993KIuwerAcademicPublishers. Printedin theNetherlands. Corrigendum Jaroslav Negetfil and Vojtech Rrdl: 'Complexity of diagrams', Order 3 (1987), 321-330. In [1] we claimed the following: THEOREM 1. The following decision problem is NP-hard. Instance: (undirected) graph G. Question: Is G a (Hasse) diagram of a poser? The reduction given in [1] from chromatic number has a gap and in fact only the following implications were proved: x(G) < 4 implies G* is a diagram; x(G) > 6 implies G* fails to be a diagram. We thank B. Toft and his student J. Thostrup who turned our attention to a gap in our argument. In [2] we described the argument which follows the same basic scheme of the proof as in [1], but it involves a recent result of Lund and Yannakakis [3] on NP-hardness of approximation of chromatic number. More specifically, for a given k, we give a polynomial construction which assigns to a graph G a diagram G; with the following properties: if x(G) ~< 4 then G~ is a diagram, if X(G)/> 4k + 1 then G~ fails to be a diagram. In January 1993, we submitted an erratum describing the construction and stating http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Order Springer Journals

Complexity of diagrams

Nešetřil, Jaroslav; Rödl, Vojtech
Order , Volume 10 (4) – Jan 21, 2005
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Complexity of diagrams

Abstract

Order 10: 393, 1993. 393 © 1993KIuwerAcademicPublishers. Printedin theNetherlands. Corrigendum Jaroslav Negetfil and Vojtech Rrdl: 'Complexity of diagrams', Order 3 (1987), 321-330. In [1] we claimed the following: THEOREM 1. The following decision problem is NP-hard. Instance: (undirected) graph G. Question: Is G a (Hasse) diagram of a poser? The reduction given in [1] from chromatic number has a gap and in fact only the following implications were proved: x(G) < 4 implies...
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Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Order, Lattices, Ordered Algebraic Structures; Discrete Mathematics; Algebra
ISSN
0167-8094
eISSN
1572-9273
DOI
10.1007/BF01108833
Publisher site
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Abstract

Order 10: 393, 1993. 393 © 1993KIuwerAcademicPublishers. Printedin theNetherlands. Corrigendum Jaroslav Negetfil and Vojtech Rrdl: 'Complexity of diagrams', Order 3 (1987), 321-330. In [1] we claimed the following: THEOREM 1. The following decision problem is NP-hard. Instance: (undirected) graph G. Question: Is G a (Hasse) diagram of a poser? The reduction given in [1] from chromatic number has a gap and in fact only the following implications were proved: x(G) < 4 implies G* is a diagram; x(G) > 6 implies G* fails to be a diagram. We thank B. Toft and his student J. Thostrup who turned our attention to a gap in our argument. In [2] we described the argument which follows the same basic scheme of the proof as in [1], but it involves a recent result of Lund and Yannakakis [3] on NP-hardness of approximation of chromatic number. More specifically, for a given k, we give a polynomial construction which assigns to a graph G a diagram G; with the following properties: if x(G) ~< 4 then G~ is a diagram, if X(G)/> 4k + 1 then G~ fails to be a diagram. In January 1993, we submitted an erratum describing the construction and stating

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Order – Springer Journals

Published: Jan 21, 2005

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