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

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandBegutachtung

Abstract

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.)
Originalspracheenglisch
TitelGraph Drawing and Network Visualization - 28th International Symposium, GD 2020, Revised Selected Papers
Redakteure/-innenDavid Auber, Pavel Valtr
Seiten482-489
Seitenumfang8
ISBN (elektronisch)978-3-030-68766-3
DOIs
PublikationsstatusVeröffentlicht - Feb. 2021
Veranstaltung28th International Symposium on Graph Drawing and Network Visualization: Graph Drawing 2020 - Virtuell, Kanada
Dauer: 16 Sept. 202018 Sept. 2020
https://gd2020.cs.ubc.ca/

Publikationsreihe

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Band12590 LNCS
ISSN (Print)0302-9743
ISSN (elektronisch)1611-3349

Konferenz

Konferenz28th International Symposium on Graph Drawing and Network Visualization
Land/GebietKanada
OrtVirtuell
Zeitraum16/09/2018/09/20
Internetadresse

ASJC Scopus subject areas

  • Theoretische Informatik
  • Informatik (insg.)

Fields of Expertise

  • Information, Communication & Computing

Fingerprint

Untersuchen Sie die Forschungsthemen von „Plane Spanning Trees in Edge-Colored Simple Drawings of Kn“. Zusammen bilden sie einen einzigartigen Fingerprint.

Dieses zitieren