Seven-bridge problem is one of the famous classical mathematical problems. In a park in Konigsberg, there are seven bridges connecting two islands and islands in the Fritz fritz pregl River with the river bank (pictured). Is it possible to start from any of these four places, cross each bridge only once, and then return to the starting point? Euler studied and solved this problem in 1736. He simplified the problem to the "one stroke" problem shown on the right, which proved that the above method was impossible. Hot issues in graph theory research. 65438+ K? nigsberg, Prussia. At the beginning of the 8th century, the Fritz fritz pregl River passed through this town. Naif Island is located in the river, and there are 7 bridges on the river, connecting the whole town. Local residents are keen on a difficult problem: is there a route that can cross seven bridges without repetition? This is the problem of the seventh bridge in Konigsberg. L. Euler uses points to represent islands and land, and the connecting line between two points represents the bridge connecting them, which simplifies rivers, islands and bridges into a network and turns the problem of seven bridges into a problem of judging whether the connected networks can draw a sum. He not only solved this problem, but also gave the necessary and sufficient conditions for connected networks to be brushes, if they are connected and the odd vertices (the number of arcs passing through this point is odd) are 0 or 2. When Euler visited Konigsberg, Prussia (now Kaliningrad, Russia) in 1736, he found that local citizens were engaged in a very interesting pastime. In konigsberg, a river called Pregel runs through it. This interesting pastime is to walk across all seven bridges on Saturday. Each bridge can only cross once, and the starting point and the ending point must be in the same place. Euler regarded every land as a point, and the bridge connecting the two lands was represented by a line. It was later inferred that such a move was impossible. His argument is this: In addition to the starting point, every time a person enters a piece of land (or point) from one bridge, he or she also leaves the point from another bridge. So every time you pass a point, two bridges (or lines) are counted, and the line leaving from the starting point and the line finally returning to the starting point are also counted, so the number of bridges connecting each piece of land and other places must be even. The graph formed by the seven bridges does not contain even numbers, so the above tasks cannot be completed. Euler's consideration is very important and ingenious, which embodies the uniqueness of mathematicians in dealing with practical problems-abstracting a practical problem into a suitable "mathematical model". This research method is called "mathematical model method". You don't need to use profound theories, thinking is the key to solving problems. Next, based on a theorem in the network, Euler quickly judged that it was impossible not to visit the seven bridges in Konigsberg at one time. In other words, for many years, the non-repetitive route that people have worked so hard to find simply does not exist. A question that stumped so many people turned out to be such an unexpected answer! 1736, Euler expounded his method of solving problems in the paper report of "Seven Bridges in Konigsberg" submitted to Petersburg Academy of Sciences. His ingenious solution laid the foundation for the establishment of a new branch of mathematics-topology. Seven Bridges and euler theorem. Through the study of seven bridges, Euler not only satisfactorily answered the questions raised by the residents of Konigsberg, but also drew and proved three more extensive conclusions about one stroke, which people usually call euler theorem. For connected graphs, the route from a node is usually called Euler path. People usually call the Euler path back to the starting point the Euler path. Graphs with Euler paths are called Euler graphs. This topic is included in "Primary Mathematics" published by People's Education Publishing House, Volume 12, page 95.