A colorful theorem on transversal lines to plane convex sets

• DOI: 10.1007/s00493-008-2385-y
• Publication Date: 2008-08-08T04:03:43Z
• Authors: Jorge L. Arocha; Javier Bracho; Luis Montejano
• Keywords: 0101 mathematics; 01 natural sciences

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.