Plane Spanning Trees in Edge-Colored Simple Drawings of Kn

Oswin Aichholzer, Michael Hoffmann, Johannes Obenaus, Rosna Paul, Daniel Perz, Nadja Seiferth, Birgit Vogtenhuber, Alexandra Weinberger

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


Károlyi, Pach, and Tóth proved that every 2-edge-colored straight-line drawing of the complete graph contains a monochromatic plane spanning tree. It is open if this statement generalizes to other classes of drawings, specifically, to simple drawings of the complete graph. These are drawings where edges are represented by Jordan arcs, any two of which intersect at most once. We present two partial results towards such a generalization. First, we show that the statement holds for cylindrical simple drawings. (In a cylindrical drawing, all vertices are placed on two concentric circles and no edge crosses either circle.) Second, we introduce a relaxation of the problem in which the graph is k-edge-colored, and the target structure must be hypochromatic, that is, avoid (at least) one color class. In this setting, we show that every ⌈(n+5)/6⌉-edge-colored monotone simple drawing of Kn contains a hypochromatic plane spanning tree. (In a monotone drawing, every edge is represented as an x-monotone curve.)
Original languageEnglish
Title of host publicationGraph Drawing and Network Visualization - 28th International Symposium, GD 2020, Revised Selected Papers
EditorsDavid Auber, Pavel Valtr
Number of pages8
ISBN (Electronic)978-3-030-68766-3
Publication statusPublished - Feb 2021
Event28th International Symposium on Graph Drawing and Network Visualization: Graph Drawing 2020 - Virtuell, Canada
Duration: 16 Sept 202018 Sept 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12590 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference28th International Symposium on Graph Drawing and Network Visualization
Internet address


  • Cylindrical drawing
  • Monotone drawing
  • Plane subdrawing
  • Simple drawing

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Fields of Expertise

  • Information, Communication & Computing


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