TY - GEN
T1 - Coloring planar homothets and three-dimensional hypergraphs
AU - Cardinal, Jean
AU - Korman, Matias
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
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U2 - 10.1007/978-3-642-29344-3_11
DO - 10.1007/978-3-642-29344-3_11
M3 - Conference contribution
AN - SCOPUS:84860791166
SN - 9783642293436
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 121
EP - 132
BT - LATIN 2012
T2 - 10th Latin American Symposiumon Theoretical Informatics, LATIN 2012
Y2 - 16 April 2012 through 20 April 2012
ER -