Coloring planar homothets and three-dimensional hypergraphs

Jean Cardinal, Matias Korman

研究成果: Conference contribution

1 被引用数 (Scopus)

抄録

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.

本文言語English
ホスト出版物のタイトルLATIN 2012
ホスト出版物のサブタイトルTheoretical Informatics - 10th Latin American Symposium, Proceedings
ページ121-132
ページ数12
DOI
出版ステータスPublished - 2012
外部発表はい
イベント10th Latin American Symposiumon Theoretical Informatics, LATIN 2012 - Arequipa, Peru
継続期間: 2012 4月 162012 4月 20

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
7256 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Other

Other10th Latin American Symposiumon Theoretical Informatics, LATIN 2012
国/地域Peru
CityArequipa
Period12/4/1612/4/20

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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