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- Liu Ran
- 2013

How many different colors are sufficient to color the countries on a map in such a way that no two adjacent countries have the same color? After examining a wide variety of different planar graphs, one discovers the apparent fact that every graph, regardless of size or complexity, can be colored with just four distinct colors. The famous four color theorem,… (More)

- Liu Ran
- 2013

The P versus NP problem is a major unsolved problem in computer science. Informally, it asks whether a computer can also quickly solve every problem whose solution can be quickly verified by a computer. It was introduced in 1971 by Stephen Cook in his seminal paper "The complexity of theorem proving procedures" and is considered by many to be the most… (More)

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