TY - GEN
T1 - On the Upward Book Thickness Problem
T2 - 29th International Symposium on Graph Drawing and Network Visualization, GD 2021
AU - Bhore, Sujoy
AU - Da Lozzo, Giordano
AU - Montecchiani, Fabrizio
AU - Nöllenburg, Martin
N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85122137577&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-92931-2_18
DO - 10.1007/978-3-030-92931-2_18
M3 - Conference contribution
AN - SCOPUS:85122137577
SN - 9783030929305
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 242
EP - 256
BT - Graph Drawing and Network Visualization - 29th International Symposium, GD 2021, Revised Selected Papers
A2 - Purchase, Helen C.
A2 - Rutter, Ignaz
PB - Springer Science and Business Media Deutschland GmbH
Y2 - 14 September 2021 through 17 September 2021
ER -