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How do 9 Points Look Like in \(\mathbb {E}^3\)?

Abstract

The aim of this note is to give an elementary proof of the following fact: given three red convex sets and three blue convex sets in \(\mathrm{I\!E}^3\), such that every red intersects every blue, there is a line transversal to the reds or there is a line transversal to the blues. This is a special case of a theorem of Montajano and Karasev (Discrete Comput Geom 46(2):283–300, 2011) and generalizes, in a sense, the colourful Helly theorem due to Lovász (cf. Discrete Math 40(2,3):141–152, 1982)

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References

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Correspondence to Ricardo Strausz.

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Communicated by Victor Chepoi.

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Strausz, R. How do 9 Points Look Like in \(\mathbb {E}^3\)?. Ann. Comb. 26, 303–307 (2022). https://doi.org/10.1007/s00026-022-00568-5

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  • DOI: https://doi.org/10.1007/s00026-022-00568-5