On the upward book thickness problem: Combinatorial and complexity results

Among the vast literature concerning graph drawing and theory, linear layouts of graphs have been subject intense research over years, both from a combinatorial an algorithmic perspective. In particular, upward book embeddings directed acyclic (DAGs) form popular class with notable applications, thickness DAG is minimum number pages required by any its embeddings. A long-standing conjecture Heath, Pemmaraju, Trenk (1999) states that outerplanar DAGs bounded above constant. this paper, we show holds for subfamilies graphs, namely those whose underlying internally-triangulated outerpath or cactus, biconnected components are st-outerplanar graphs. On complexity side, it known deciding whether has k NP-hard fixed k≥3. We problem, k≥5, remains domination O(k), but fixed-parameter tractable (FPT) in vertex cover number.