The first part is a bipartite graph. As usual, many concepts are introduced, such as bipartite graph (bipartite graph), complementary vertex subset and some matching related concepts. Generally speaking, a bipartite graph can divide the vertices into two parts, and there is no edge between the vertices of each part. Matching refers to the set of non-adjacent edges, in which the concepts of maximum and maximum are divided. The maximum value refers to the match without more edges, and the maximum value refers to the match with the most edges among all matches.
The second section is about Euler. Speaking of Euler, it can be traced back to the problem of18th century. It is about whether there is a ring between seven bridges on four islands that only passes through each side once. Euler found a solution to this problem, so there is such a thing as Euler path. Graphs with Euler paths can be called Euler graphs.
The third section is hamiltonian graph, which is very interesting and just corresponds to the Euler path. Hamilton loop refers to a loop that passes through each node in the graph and only passes once. Its main fire point is the node, not the edge, and the graph satisfying Hamilton cycle is called Hamilton graph.
The fourth part is the plan. I always feel funny when I read this chapter. Whether it is bipartite graph, Euler graph or Hamilton graph, their names are confusing at first glance, but in fact they are as simple as explosion. The plan is impartial, on the contrary. Refers to whether edges can't intersect except vertices through different painting methods. If so, this diagram is a plan, and the drawing method you realize is called plane embedding. There are necessary and sufficient conditions related to the plan, which can be deeply understood when using.