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-hard for any fixed k≥ 3. We show that the problem, for any k≥ 5, remains NP-hard for graphs whose domination number is O(k), but it is FPT in the vertex cover number.
Bhore, S., Da Lozzo, G., Montecchiani, F., Nollenburg, M. (2021). On the Upward Book Thickness Problem: Combinatorial and Complexity Results. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp.242-256). Springer Science and Business Media Deutschland GmbH [10.1007/978-3-030-92931-2_18].
On the Upward Book Thickness Problem: Combinatorial and Complexity Results
Da Lozzo G.
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2021-01-01
Abstract
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-hard for any fixed k≥ 3. We show that the problem, for any k≥ 5, remains NP-hard for graphs whose domination number is O(k), but it is FPT in the vertex cover number.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
