**
Path in Complete Geometric Graphs**

A

*geometric graph* is a graph drawn in the plane such that

*a)*
no three vertices are colinear and

*b)* edges are straight line segments.
Edges are allowed to cross, but only transversally at interior points.
A complete geometric graph is a geometric drawing of

*K_n*.

**Problem:** *Is there a constant *c* such that for any 2-coloring
of the edges of a complete geometric graph on *n* vertices, there
is a monochromatic path of length at least *cn*?*

I do not have references for this problem.

Submitted by: Dan Archdeacon, Dept. of Math. and
Stat.,

University of Vermont,

Burlington, VT 05401-1455 USA
Send comments to *dan.archdeacon@uvm.edu*

December 2003