2005/07/06 by I. Cahit, Cahit, I. · 1 citation
Computer Science · Mathematics · #05C #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications #math.CO #msc:05C
paper · pdf · doi:10.48550/arxiv.math/0507127
draft-paper, 14 pages, 8 figures
arxiv created 2005/07/06 · openalex publication_date 2005/07/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.