On the Upward Book Thickness Problem: Combinatorial and Complexity Results

Sujoy Bhore, Giordano Da Lozzo, Fabrizio Montecchiani, Martin Nöllenburg

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

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.

Original languageEnglish
Title of host publicationGraph Drawing and Network Visualization - 29th International Symposium, GD 2021, Revised Selected Papers
EditorsHelen C. Purchase, Ignaz Rutter
PublisherSpringer Science and Business Media Deutschland GmbH
Pages242-256
Number of pages15
ISBN (Print)9783030929305
DOIs
StatePublished - 1 Jan 2021
Externally publishedYes
Event29th International Symposium on Graph Drawing and Network Visualization, GD 2021 - Tübingen, Germany
Duration: 14 Sep 202117 Sep 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12868 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference29th International Symposium on Graph Drawing and Network Visualization, GD 2021
Country/TerritoryGermany
CityTübingen
Period14/09/2117/09/21

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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