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**On the complexity of diagram testing.**
*(English)*
Zbl 0808.06003

Summary: J. Nešetřil and V. Rödl [ibid. 3, 321-330 (1987; see the review below)] claim to have proved that the problem of finding whether a given graph \(G\) can be oriented as the diagram of a partial order is NP-complete. A flaw was discovered in their proof by J. Thostrup [Partially ordered sets and graphs (Danish), MSc. Diss., Odense Univ. (1992)]. J. Nešetřil and V. Rödl [“More on complexity of diagrams”, submitted to Order] have since corrected the proof, but the new version is rather complex. We give a simpler and more elementary proof, using a completely different approach.

### MSC:

06A06 | Partial orders, general |

68Q25 | Analysis of algorithms and problem complexity |

05C75 | Structural characterization of families of graphs |

Full Text:
DOI

### References:

[1] | M. R. Garey and D. S. Johnson (1979)Computers and Intractability: A Guide to the Theory of NP-completeness, Freeman. · Zbl 0411.68039 |

[2] | C. Lund and M. Yannakakis (1993) On the hardness of approximating minimization problems, in25th ACM Symposium on the Theory of Computing, pp. 286-293. · Zbl 1310.68094 |

[3] | K. M. Mosesian (1972) Certain theorems on strongly basable graphs [Russian],Akad. Nauk Armian. SSR Dokl. 55, 83-86. |

[4] | J. Ne?et?il and V. R?dl (1987) Complexity of diagrams,Order 3, 321-330. · Zbl 0808.06004 · doi:10.1007/BF00340774 |

[5] | J. Ne?et?il and V. R?dl, More on complexity of diagrams, submitted toOrder. |

[6] | O. Ore (1962)Theory of Graphs, AMS Coll. Publ.34, Providence, RI. · Zbl 0105.35401 |

[7] | O. Pretzel (1985) On graphs that can be oriented as diagrams of ordered sets,Order 2, 25-40. · Zbl 0571.05041 · doi:10.1007/BF00337921 |

[8] | O. Pretzel (1986) On reorienting graphs by pushing down maximal vertices,Order 3, 135-153. · Zbl 0611.05028 · doi:10.1007/BF00390104 |

[9] | O. Pretzel (1986) Orientations and reorientations of graphs,Cont. Math. 57, 103-125. · Zbl 0595.06005 |

[10] | O. Pretzel and D. Youngs (1991) Balanced graphs and noncovering graphs,Disc. Math. 88, 279-287. · Zbl 0764.05095 · doi:10.1016/0012-365X(91)90015-T |

[11] | J. Thostrup (1992) Partial ordered sets and graphs (in Danish), MSc. dissertation, Odense University, Denmark, 56 pp. |

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