On the curve complexity of 3-colored point-set embeddings

Emilio Di Giacomo, Leszek Gąsieniec, Giuseppe Liotta, Alfredo Navarra

Research output: Contribution to journalArticlepeer-review

Abstract

We establish new results on the curve complexity of k-colored point-set embeddings when k=3. We show that there exist 3-colored caterpillars with only three independent edges whose 3-colored point-set embeddings may require [Formula presented] bends on [Formula presented] edges. This settles an open problem by Badent et al. [5] about the curve complexity of point set embeddings of k-colored trees and it extends a lower bound by Pach and Wenger [35] to the case that the graph only has O(1) independent edges. Concerning upper bounds, we prove that any 3-colored path admits a 3-colored point-set embedding with curve complexity at most 4. In addition, we introduce a variant of the k-colored simultaneous embeddability problem and study its relationship with the k-colored point-set embeddability problem.

Original languageEnglish (US)
Pages (from-to)114-140
Number of pages27
JournalTheoretical Computer Science
Volume846
DOIs
StatePublished - Dec 18 2020
Externally publishedYes

Keywords

  • Graph drawing
  • Point-set embedding
  • Simultaneous embedding

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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