  In this paper we have shown without assuming the four color theorem of planar
graphs that every (bridgeless) cubic planar graph has a three-edge-coloring.
This is an old-conjecture due to Tait in the squeal of efforts in settling the
four-color conjecture at the end of the 19th century. We have also shown the
applicability of our method to another well-known three edge-coloring
conjecture on cubic graphs. Namely Tutte's conjecture that "every 2-connected
cubic graph with no Petersen minor is 3-edge colorable". Hence the conclusion
of this paper implies another non-computer proof of the four color theorem by
using spiral-chains in different context.
