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2015

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… Expand

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2012

2012

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

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2009

2009

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

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2004

2004

We prove τodd(G) ≤ 2Vodd(G) for each planar graph G where vodd(G) is the maximum number of edge-disjoint odd cycles and τodd(G… Expand

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2002

2002

Based on a representation of primitive proof objects as λ-terms, which has been built into the theorem prover Isabelle recently… Expand

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2002

2002

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

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2000

2000

Abstract In this note, we show that the edges and faces of any plane graph with maximum degree three can be simultaneously… Expand

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1981

1976

1975

1975

Let f 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… Expand

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