The five color theorem is a result from graph theory that given a plane separated into regions, such as a political map of the counties of a state… (More)

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2015

2015

- Fu Yuhua
- 2015

With the help of Neutrosophy and Quad-stage Method, the proof for negation of “the four color theorem” is given. In which the key… (More)

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2012

2012

- Min Jae Song
- 2012

In this paper, we will define the necessary concepts to formulate map coloring problems. Then, we will prove Euler’s formula and… (More)

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2010

2010

Let / be a face of a plane graph G. The Three and Five Color Theorem proved here states that the vertices of G can be colored… (More)

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2009

2009

- Limin Xiang
- ArXiv
- 2009

A formal proof has not been found for the four color theorem since 1852 when Francis Guthrie first conjectured the four color… (More)

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2009

2009

- Bogdan Oporowski, David X Zhao
- Discrete Mathematics
- 2009

We generalize the Five Color Theorem by showing that it extends to graphs with two crossings. Furthermore, we show that if a… (More)

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Highly Cited

2002

Highly Cited

2002

In this paper, we introduce graph theory, and discuss the Four Color Theorem. Then we prove several theorems, including Euler’s… (More)

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2000

1998

1998

- Robin Thomas
- 1998

848 NOTICES OF THE AMS VOLUME 45, NUMBER 7 E very planar map of connected countries can be colored using four colors in such a… (More)

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1984

1984

We prove that if a graph embeds on a surface with all edges suitably short, then the vertices of the graph can be five-colored… (More)

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