For a point in the graph, if the number of lines entering and leaving this point is odd, it is odd, even if it is even.
So, a picture can draw a condition is:
All even points of (1) connected graph. Take any even point as the starting point, and finally you can finish drawing this picture with this point as the end point.
(2) There are only two singularities, and the others are even-point connected graphs. One singularity must be the starting point and the other singularity must be the end point.
Extended data
/kloc-At the beginning of the 8th century, there was a park in Konigsberg, Prussia (now Kaliningrad, Russia). There are seven bridges in the park connecting two islands in the Fritz fritz pregl River with the river banks.
In 1736, local residents held an interesting fitness activity: on Saturday, they walked across all seven bridges, each bridge can only pass once, and the starting point and ending point must be the same place.
Many people have tried, but they all failed. At that time, Euler, the greatest mathematician in the world, happened to be here. He is keenly aware that there is a profound mathematical connotation here, which is called the problem of one stroke.
Euler drew seven lines on seven bridges, turning the question into whether this figure can be drawn in one stroke. Euler wanted to think, feel impossible. Not only that, Euler also got the conditions of which graphics can be drawn and which can't be drawn.
Through the study of seven bridges, Euler not only satisfactorily answered the questions raised by Konigsberg residents, but also drew and proved three more extensive conclusions about a stroke, which people usually call "euler theorem F".
Baidu Encyclopedia-Seven Bridges Problem
Baidu encyclopedia-one trick