沈阳理工大学学士学位论文

part of the machine.

1 Combinatorial Mathematics Problems in Classic

The classic of combinatorial mathematics problems include: (1) perfect cover board; (2) the cutting cube; Magic square (3); Four color (4); (5) problems 36 officer; 6 the shortest path; 7 NIM take son problem; 8) sheep Wolf food across the river; 9) China the postman problem; ⑩ stable marriage problems. The following key introduced four color problem and China the postman problem.

More than a century, the study of four color proof process, because the object complex and lack of mathematics usually work standards, artificial direct verification is not workable. In the 70 s. The electronic computer the rapid development and application of four color make the research appeared turnaround. The university of Illinois upper, hawking in various ways to prove the former research and the ideas of foundation, since 1972, started with the computer four color proof of research work. Finally in 1976 thoroughly solved the problem of four colors, the whole process in computer proof spent 1200 hours. Four color map problem is the first mainly by the computer to complete the proof of the math problems. Scientists in the study and solve the problems of four color, also from which many new mathematical theory, the development of the many mathematics calculation method, stimulate the topology and graph theory development.

1.1 Four-color problem

Four-color problem using four different colors on the world map coloring. Requirements of the color of the neighboring countries are different. The use of mathematical language is formally described as follows: a plane arbitrarily subdivided into area not overlap, each region can always be 1, 2, 3, 4, 4 one of the digital tag, but not accounted for on the question the two regions adjacent to make the same number.

More than a century, studies have shown that four-color problem, because the object

41

沈阳理工大学学士学位论文

complexity of the problem and the lack of the usual mathematical problem solving norms, artificial direct verification is not feasible. The 1970s. The rapid development and wide application of the computer so that the four-color problem of a turning point. Appel, Haken of the University of Illinois in the basis of the previous kinds of proof methods and ideas, since 1972, and began research work with a computer to prove the four color problem. In 1976, completely solve the four-color problem, the entire certification process has spent 1200 hours on the computer. Map of four-color problem is the first major completion certificate by the computer mathematical problems. Scientists in research and solve the problem of four-color process, but also the resulting number of new mathematical theory, development of mathematical methods to stimulate the development of topology and graph theory.

1.2 China the Postman Problem

A postman work is: according to certain route he is responsible for delivering the block of the street every E-mail, and back to the post office, ask the postman must cross the street he is responsible for every street is at least once, and hope to choose a total distance of the shortest delivery routes. Looking for such a shortest delivery route, issues in the international academic community called China the postman problem, because it is sponsored by China in 1962 GuanMei mathematician operator’s professor, first proposed and studied.

1.21 Euler circuit problem

Theorem of l connected graph G (V, E), including V said in the chart the node set, E said edge set, then the following conditions are mutually equivalent: (1) G is a European pulling the; (2) the G each node is the even degree; (3) the edge of G can be decomposed into several set E circuit and.

1.2.2 The solution of the Euler circuit

42

沈阳理工大学学士学位论文

Cycle of find the starting point. A node from the start, and then find out a starting from the back to the point of ring path. This method to ensure that every edge are traverse. If there is a point of edge is not traverse let this point as a starting point, this side for start edge, and the current ring cohesion. So until all the edge were traverses. That way, the whole figure will be connected together.

Theorem 2 connected to existing eular circuit diagram is the necessary and sufficient conditions for the foot of any node, entering the city at the number (into several) and out the side of the point number (three-dimensional) are equal.

1.2.3 Postman Problem Solving

Use of the graph theory of language, save a connected empowerment nets G (V, E), to find a loop, and makes the circuit contains G towel at least once each side, and the weight of the circuit smallest. That is to contain the G each from the edge of the loop to find a minimum weight of the Internet.

If G is euler figure, if the figure that Europe has a loop, the you for the \loop all, so any a eular circuit for this problem is the solution, it is very easy to described in section 1.1.2 by luo lai algorithm for the Florida a eular circuit for, but if the G not euler figure, there is a strange degree. Node, then China the postman to the solution of the problem to much more difficult. Interested readers can as reference.

2 Computer Science and Combinatorial Mathematics

Along with the juice the further development of the computer technology, especially the widespread use of computer network, the use of computers has been deeply to scientific research and People's Daily life in all areas. The computer to do more intelligent to development, its way out is still the algorithm of mathematics and math mechanization. Algorithm of computer science research is an important research field, combination mathematicians in the early 1970 s established algorithm complexity theory of computer

43

沈阳理工大学学士学位论文

algorithm for NP in research on the complexity of the important theoretical foundation to provide. Combinatorial mathematics is the computer industry. Development of high level software products without combinatorial mathematics.

Combinatorial mathematics in the week has been a very important subject, even is the foundation of computer science, this computer science authorities many is the research combinatorial mathematics was born. The United States and India in the software industry is a world leading position, and the two countries in the basic math. Especially the combinatorial mathematics talents reserves inseparable, but still have a man in China to combinatorial mathematics understanding is not enough, think combinatorial mathematics is just a kind of pure fundamental subject, practical significance to economic development is not big, but the actual situation of the software industry, network algorithms and analysis, information compression, network security, coding technology, system software is inseparable from the combinatorial mathematics theory and method of the support. With the basic mathematics for the study on the basic theory of the development of the software industry in our country has become a bottleneck, China to want to can become a software superpower, we need to strengthen the combinatorial mathematics teaching and personnel training, etc. research organization, and founded the first combination mathematics in China international journal annual combination \In addition, Tsinghua University, China University of science and technology, Tongji University, key university also established the key laboratory research combinatorial mathematics. In short, in recent years, China's combination mathematics basic research work by the university and the masses of scientific workers more and more attention, especially in university students' mathematical modeling competition between the carry out activities, improve the students' computer technology with the ability to solve practical problems, also greatly stimulate the students' mathematics knowledge of combination of demand, motivated the combination of learning mathematics boom.

3 Conclusions

With the popularity of computer promotion, combinatorial mathematics this of the oldest

44