  In this paper we have given a unified graph coloring algorithm for planar
graphs. The problems that have been considered in this context respectively,
are vertex, edge, total and entire colorings of the planar graphs. The main
tool in the coloring algorithm is the use of spiral chain which has been used
in the non-computer proof of the four color theorem in 2004. A more precies
explanation of the proof of the four color theorem by spiral chain coloring is
also given in this paper. Then we continue to spiral-chain coloring solutions
by giving the proof of other famous conjectures of Vizing's total coloring and
planar graph conjectures of maximum vertex degree six. We have also given the
proof of a conjecture of Kronk and Mitchem that any plane graph of maximum
degree "Delta" is entirely ("Delta"+4)-colorable.The last part of the paper
deals with the three colorability of planar graphs under the spiral chain
coloring. We have given an efficient and short proof of the Groetzsch's Theorem
that triangle-free planar graphs are 3-colorable.
