A proof that any bridgeless planar graph can have faces properly four-colored. The proof has a lemma ten parts and three appendices; it uses edges of three values and has six figures.
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OUR NEW PROOF OF THE FOUR-COLOR GRAPH THEOREM | fourcolorgraph.net Reviews
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A proof that any bridgeless planar graph can have faces properly four-colored. The proof has a lemma ten parts and three appendices; it uses edges of three values and has six figures.
fourcolorgraph.net
ACKNOWLEDGMENTS
http://www.fourcolorgraph.net/ACKNOWLEDGMENTS.html
Our email address is rbamford2@earthlink.net. If your message does not appear in your SENT file please resend message to rbamford2@earthlink.net using your web interface. Suggestions on how to get referred journals to consider improved versions of our theorem would be appreciated. Additional Figures can be sent if requested.
Short Proof
http://www.fourcolorgraph.net/SHORT_PROOF.html
Every Planar Bridgeless Graph is Four-colorable. Robert M. Bamford. Planar cubic bridgeless graphs, with colorings that do not have two edges of the same value extending to any vertex are considered. Also there are only three edge values except for edges of one face. The exceptional face is pentagonal, represented in figures as the surrounding face. A Lemma proposes that colorings of considered graphs require only three values for edges including edges of the pentagon, unless the coloring has. Graphs (G)...
Graph in Proof
http://www.fourcolorgraph.net/GRAPH_IN_PROOF.html
The seventeen face graph with four of its colorings shown on the right has many interesting properties which are the basis of a new proof of the four-color graph theorem. The graph can easily be colored with only four colors including the surrounding face as seen in the coloring on our HOME. Page Some colorings like the four colorings shown on the right appear to have only four colors. Each such coloring has a fifth color, the color of the surrounding face. Our email address is rbamford2@earthlink.net.
About Authors
http://www.fourcolorgraph.net/ABOUT_AUTHORS.html
Our email address is rbamford2@earthlink.net. If your message does not appear in your SENT file please resend message to rbamford2@earthlink.net using your web interface. Suggestions on how to get referred journals to consider improved versions of our theorem would be appreciated. Additional Figures can be sent if requested.
ACKNOWLEDGMENTS
http://www.fourcolorgraph.net/abstract.html
Every Planar Bridgeless Graph is Four-colorable. Planar cubic bridgeless graphs, with edges of only three values except for edges of one pentagonal face, are considered. No two edges to any vertex have the same value. Considered graphs require edges of only three values including edges of the pentagon unless every coloring has the obstacle identified in a lemma. The following statements are proven. Considered graphs with. Our email address is rbamford2@earthlink.net.
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OUR NEW PROOF OF THE FOUR-COLOR GRAPH THEOREM
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