Coloring planar homothets and three-dimensional hypergraphs

Jean Cardinal; Matias Korman

doi:10.1007/978-3-642-29344-3_11

Coloring planar homothets and three-dimensional hypergraphs

Jean Cardinal, Matias Korman

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	LATIN 2012
Subtitle of host publication	Theoretical Informatics - 10th Latin American Symposium, Proceedings
Pages	121-132
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-29344-3_11
Publication status	Published - 2012
Externally published	Yes
Event	10th Latin American Symposiumon Theoretical Informatics, LATIN 2012 - Arequipa, Peru Duration: 2012 Apr 16 → 2012 Apr 20

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	7256 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	10th Latin American Symposiumon Theoretical Informatics, LATIN 2012
Country	Peru
City	Arequipa
Period	12/4/16 → 12/4/20

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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10.1007/978-3-642-29344-3_11

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Cardinal, J., & Korman, M. (2012). Coloring planar homothets and three-dimensional hypergraphs. In LATIN 2012: Theoretical Informatics - 10th Latin American Symposium, Proceedings (pp. 121-132). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7256 LNCS). https://doi.org/10.1007/978-3-642-29344-3_11

Coloring planar homothets and three-dimensional hypergraphs. / Cardinal, Jean; Korman, Matias.

LATIN 2012: Theoretical Informatics - 10th Latin American Symposium, Proceedings. 2012. p. 121-132 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7256 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Cardinal, J & Korman, M 2012, Coloring planar homothets and three-dimensional hypergraphs. in LATIN 2012: Theoretical Informatics - 10th Latin American Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7256 LNCS, pp. 121-132, 10th Latin American Symposiumon Theoretical Informatics, LATIN 2012, Arequipa, Peru, 12/4/16. https://doi.org/10.1007/978-3-642-29344-3_11

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Coloring planar homothets and three-dimensional hypergraphs

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