Spiral Chains: The Proofs of Tait's and Tutte's Three-Edge-Coloring Conjectures

Details Spiral Chains: The Proofs of Tait's and Tutte's Three-Edge-Coloring Conjectures Spiral Chains: The Proofs of Tait's and Tutte's Three-Edge-Coloring Conjectures

2005-07-06

arxiv.org/abs/math/0507127v1

Mathematics

Combinatorics

draft-paper, 14 pages, 8 figures

Scientific paper

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.

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