A colorful theorem on transversal lines to plane convex sets

Abstract

We prove a colorful version of Hadwiger’s transversal line theorem: if a family of colored and numbered convex sets in the plane has the property that any three differently colored members have a transversal line that meet the sets consistently with the numbering, then there exists a color such that all the convex sets of that color have a transversal line.

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Correspondence to Jorge L. Arocha.

Additional information

All authors are partially supported by CONACYT research grant 5040017.

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Arocha, J.L., Bracho, J. & Montejano, L. A colorful theorem on transversal lines to plane convex sets. Combinatorica 28, 379 (2008). https://doi.org/10.1007/s00493-008-2385-y

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Mathematics Subject Classification (2000)

  • 52A35