On the Upward Book Thickness Problem: Combinatorial and Complexity Results

  title={On the Upward Book Thickness Problem: Combinatorial and Complexity Results},
  author={Sujoy Kumar Bhore and Giordano Da Lozzo and Fabrizio Montecchiani and Martin N{\"o}llenburg},
  booktitle={International Symposium Graph Drawing and Network Visualization},
A long-standing conjecture by Heath, Pemmaraju, and Trenk states that the upward book thickness of outerplanar DAGs is bounded above by a constant. In this paper, we show that the conjecture holds for subfamilies of upward outerplanar graphs, namely those whose underlying graph is an internally-triangulated outerpath or a cactus, and those whose biconnected components are st-outerplanar graphs. On the complexity side, it is known that deciding whether a graph has upward book thickness k is NP… 

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