metric graphs or distance graphs are graphs G(M;D) where M is a subset
of a metric space and D is a set of positive numbers; two vertices
are connected by an edge if their distance lies in D. One of the
most famous distance graphs is the unit distance graph G(R^2;{1}).
Two "close" relatives are the integral distance graph G(R^2;Z+) and the
odd distance graph G(R^2; {2n + 1, n = 1, 2,.. }). The odd distance graph
was "launched" in 1994 by Paul Erdos. At the outset, we wondered how close
are the unit distance graph and the odd distance graph, we now know that
they are very far apart. In this talk I will discuss the latest results
in the pursuit of uncovering the mysteries of the odd distance graph:
Its chromatic number is at least 5, no upper bound is known.
