Recognizing DAGs with Page-Number 2 Is NP-complete

The page-number of a directed acyclic graph (a DAG, for short) is the minimum k which DAG has topological order and k-coloring its edges such that no two same color cross, i.e., have alternating endpoints along order. In 1999, Heath Pemmaraju conjectured recognition DAGs with 2 NP-complete proved recognizing 6 [SIAM J. Computing, 1999]. Binucci et al. recently strengthened this result by proving NP-complete, every $$k\ge 3$$ [SoCG 2019]. paper, we finally resolve Pemmaraju’s conjecture in affirmative. particular, our NP-completeness holds even st-planar graphs planar posets.