[Plan Theory] Plan Study Notes, Plan Theory Study Notes

[Plan Theory] Plan Study Notes, Plan Theory Study Notes

Why should I learn the plan now?
Because the plane plan was determined by Shun-cutting HNOI2010...

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First, there are some definitions:

What is a floor plan?
For a graph G = <V, E>, if you can draw G on a plane and any two sides of the drawn graph have no intersection points except the nodes in V, the graph G is a plan.
PlanSurface:
For a plan, if some edges are enclosed and the area does not contain the vertices and edges of the plan, this area is called a plane of the plan.
For example, the red area is as follows:

We call it a circle composed of the edges in this area.BoundaryThe length of the. boundary is called this surface.Degrees.
We define a surface set F, so we can represent it as G = <V, E, F>
The nature of the plan (for details and proofs, see Liu cailiang, 2003 paper of the national training team, "application of the plan in informatics"):

1. if graph G = <V, E, F> is a connected plan, Σ f ε F d (f) = 2 | E |
2. If graph G = <V, E, F> is a connected plan, | V | − | E | + | F | = 2

Of course, for an unconnected plan, we can break it down into several Unicom blocks and establish each of these two attributes (this is obvious ), therefore, we can obtain some properties of the unconnected plan. I will not go into details here.
The following inferences can be obtained from the above two properties:

For a given connected simple plan G = <V, E, F>, if | V |> = 3, then | E | <= 3 | V |-6, | F | <= 2 | V |-4

I think there is something wrong with the second inference of the original article. Anyway, the second one seems to beUseless
The role of the first inference is to tell us that the order of magnitude E is O (| V |...

Plan determination (That's why I learned the plan.):
Practice