Any connected graph composed of even points can be drawn with one stroke, and any even point can be used as the starting point when drawing, and finally the graph can be completed with this point as the end point; Connected graphs with only two singularities are even points and can be drawn with one stroke. When drawing, one singularity must be the starting point and the other singularity must be the end point. Other situations can't be drawn in one stroke.
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/kloc-one of the famous classical mathematical problems in the 0/8th century. 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.