  The chromatic number of an planar graph is not greater than four and this is
known by the famous four color theorem and is equal to two when the planar
graph is bipartite. When the planar graph is even-triangulated or all cycles
are greater than three we know by the Heawood and the Grotszch theorems that
the chromatic number is three. There are many conjectures and partial results
on three colorability of planar graphs when the graph has specific cycles
lengths or cycles with three edges (triangles) have special distance
distributions. In this paper we have given a new three colorability criteria
for planar graphs that can be considered as an generalization of the Heawood
and the Grotszch theorems with respect to the triangulation and cycles of
length greater than 3. We have shown that an triangulated planar graph with
disjoint holes is 3-colorable if and only if every hole satisfies the parity
symmetric property, where a hole is a cycle (face boundary) of length greater
than 3.
