Planar Drawings with Few Slopes of Halin Graphs and Nested Pseudotrees

S. Chaplick, Giordano Da Lozzo*, Emilio Di Giacomo, Giuseppe Liotta, Fabrizio Montecchiani

*Corresponding author for this work

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

Abstract

The planar slope number psn(G) of a planar graph G is the minimum number of edge slopes in a planar straight-line drawing of G. It is known that psn(G) epsilon O(c(Delta)) for every planar graph G of degree Delta. This upper bound has been improved to O(Delta(5)) if G has treewidth three, and to O(Delta) if G has treewidth two. In this paper we prove psn(G) epsilon Theta(Delta) when G is a Halin graph, and thus has treewidth three. Furthermore, we present the first polynomial upper bound on the planar slope number for a family of graphs having treewidth four. Namely we show that O(Delta(2)) slopes suffice for nested pseudotrees.
Original languageEnglish
Title of host publicationALGORITHMS AND DATA STRUCTURES, WADS 2021
EditorsA Lubiw, M Salavatipour
PublisherSpringer Nature
Pages271-285
Number of pages15
Volume12808
ISBN (Print)9783030835071
DOIs
Publication statusPublished - 2021
Event17th International Symposium on Algorithms and Data Structures - Online, Dalhousie University, Halifax, Canada
Duration: 9 Aug 202111 Aug 2021
Conference number: 17
https://projects.cs.dal.ca/wads2021/

Publication series

SeriesLecture Notes in Computer Science
Volume12808
ISSN0302-9743

Conference

Conference17th International Symposium on Algorithms and Data Structures
Abbreviated titleWADS 2021
Country/TerritoryCanada
CityHalifax
Period9/08/2111/08/21
Internet address

Cite this