Tightness problems in the plane Original Research Article

A 3-uniform hypergraph is called tight if for any 3-coloring of its vertex set a heterochromatic edge can be found. In this paper we study tightness of 3-graphs with vertex set R2 and edge sets arising from simple geometrical considerations. Basically, we show that sets of triangles with ‘fat shadows’ are tight and also that some interesting sets of triangles with ‘thin shadows’ are tight.