## Abstract

The page-number of a directed acyclic graph (a DAG, for short) is the minimum k for which the DAG has a topological order and a k-coloring of its edges such that no two edges of the same color cross, i.e., have alternating endpoints along the topological order. In 1999, Heath and Pemmaraju conjectured that the recognition of DAGs with page-number 2 is NP-complete and proved that recognizing DAGs with page-number 6 is NP-complete [SIAM J. Computing, 1999]. Binucci et al. recently strengthened this result by proving that recognizing DAGs with page-number k is NP-complete, for every k≥3

[SoCG 2019]. In this paper, we finally resolve Heath and Pemmaraju’s conjecture in the affirmative. In particular, our NP-completeness result holds even for st-planar graphs and planar posets.

[SoCG 2019]. In this paper, we finally resolve Heath and Pemmaraju’s conjecture in the affirmative. In particular, our NP-completeness result holds even for st-planar graphs and planar posets.

Original language | English |
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Title of host publication | Graph Drawing and Network Visualization - 30th International Symposium, GD 2022, Tokyo, Japan, September 13-16, 2022, Revised Selected Papers |

Editors | Patrizio Angelini, Reinhard von Hanxleden |

Publisher | Springer |

Pages | 361-370 |

Number of pages | 10 |

Volume | 13764 |

DOIs | |

Publication status | Published - 2022 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |