'Color theorem' presentation slideshows

Planar Graphs

Planar Graphs. The clique on 4 nodes. A graph is called planar if it can be drawn in the plane in such a way that no two edges cross. Example of a planar graph:. A graph is called planar if it can be drawn in the plane in such a way that no two edges cross. Example of a planar graph:.

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Planar Graphs

Great Theoretical Ideas In Computer Science. Planar Graphs. Lecture 22. CS 15-251. The clique on 4 nodes. A graph is called planar if it can be drawn in the plane in such a way that no two edges cross. Example of a planar graph:.

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Some applications of graph theory

Some applications of graph theory. More on the Four Color Problem. The four color theorem was stated, but not proved, in 1853 by Francis Guthrie. The theorem asserts that four colors are enough to color any geographical map in such a way that no neighboring two countries are of the same color.

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Graph Theory in Networks

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Milena Mihail mihail@cc.gatech.edu

Discussion Topic:. Models for Social Networks. Web Science Tea Feb 29, 08. Milena Mihail mihail@cc.gatech.edu. NSF : CDI. Elsewhere :. Yahoo: Raghavan WWW06 Brachman GT talk. Microsoft :

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Theorem 6.3.1

Theorem 6.3.1. Every planar graph is 5-colorable. Proof. 1. We use induction on n(G), the number of nodes in G. 2. Basis Step: All graphs with n(G) ? 5 are 5-colorable. 3. Induction Step: n(G) > 5. 4. G has a vertex, v, of degree at most 5

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Modeling Using Colorability

Modeling Using Colorability. Presented by: Kelley Louie CSC 252 Algorithms 252a-aj. Introduction. All of the algorithms that we have learned in class have real world applications such as social science problems.

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The Four Color Theorem (4CT)

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How many colors does it take to color a map so no two regions have the same color?

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