Coloring planar homothets and three-dimensional hypergraphs

Jean Cardinal, Matias Korman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

We prove that every finite set of homothetic copies of a given compact and convex body in the plane can be colored with four colors so that any point covered by at least two copies is covered by two copies with distinct colors. This generalizes a previous result from Smorodinsky (SIAM J. Disc. Math. 2007). Then we show that for any κ ≥ 2, every three-dimensional hypergraph can be colored with 6(κ-1) colors so that every hyperedge e contains min {|e|,κ} vertices with mutually distinct colors. This refines a previous result from Aloupis et al. (Disc. & Comp. Geom. 2009). As corollaries, we obtain constant factor improvements for conflict-free coloring, κ-strong conflict-free coloring, and choosability. Proofs of the upper bounds are constructive and yield simple, polynomial-time algorithms.

Original languageEnglish
Title of host publicationLATIN 2012
Subtitle of host publicationTheoretical Informatics - 10th Latin American Symposium, Proceedings
Pages121-132
Number of pages12
DOIs
Publication statusPublished - 2012
Externally publishedYes
Event10th Latin American Symposiumon Theoretical Informatics, LATIN 2012 - Arequipa, Peru
Duration: 2012 Apr 162012 Apr 20

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7256 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other10th Latin American Symposiumon Theoretical Informatics, LATIN 2012
CountryPeru
CityArequipa
Period12/4/1612/4/20

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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