Chapter 402

Due to the limited space of the whiteboard, the final steps are as concise as possible, so the thinking process is ignored.

But people who study Mathematical Olympiad know that the steps of solving problems are only external presentation, and the really important thing is thinking ability.

Tan Jiaxu also wants to hear how she solves the problem, how to start, and how she thinks of lemmas and nested lemmas to prove the conclusion.

Jiang Fuyue: "do you want to listen?"

"To -"

"OK."

Tan Jiaxu returned to his seat and looked up at the podium. His eyes showed his face to Jiang Fuyue for the first time.

Zou Hao was amazed.

Although I praise that I usually play with them and have a good relationship with them, there is always a sense of pride in the bones of genius.

He didn't deliberately show up, but Zou Hao felt it.

Now, I look at Jiang Fuyue with this kind of eyes

It can only show that the only genius who can convince genius is the genius among geniuses.

At this time, Jiang Fuyue had picked up her pen and stood in front of the whiteboard——

"Seeing this problem, many people's first reaction is to try to find the relationship between vertices and edges."

A large number of students nodded heavily below.

That's what they think.

"We know a connected graph. Suppose it has V vertices. If it has only V-1 edges, it is impossible to have cycles. Otherwise, this graph is not a connected graph."

"However, when we have v edges, there must be a circle. On this basis, every time we add an edge, we will create a new circle. Suppose that when we have V + 1 edges, there is only one circle in the graph, then when we remove an edge from the circle, there will be no circle in the graph, but there are still V vertices in the graph, there must be a circle "So our hypothesis is not true. There are at least two circles in the graph..."

Tan praised his focus.

Zou Hao didn't want to hear it, but the girl's voice was refreshing and cool, like a mountain spring in a deep stream.

He was attracted unconsciously.

Jiang Fuyue: "... Here we need to introduce a new definition called margin, that is, the number of edges e minus (V-1), which is equal to E-V + 1. It is used to describe the amount of redundant vertices in a graph, which roughly determines the number of circles in our graph."

Tan Jiaxu's eyes brightened.

Yes, that's it!

What he thought was how to bypass this proof point, but Jiang Fuyue directly introduced a new definition.

He avoided risks, and she went straight ahead.

This is the difference in their thinking process, which eventually leads to the distinction between success and failure.

So, he lost, not without reason.

Jiang Fuyue stood on the podium, slim and handsome, with outstanding temperament, but at this moment, almost everyone subconsciously ignored her appearance. What they saw was her luminous wisdom, strong logic, rigorous attitude, and her respect and piety for knowledge.

"... if we think further, in fact, when there are more and more edges in the graph, there will be more and more circles, and these circles will cross each other, and the circumference of the circle will be smaller and smaller. Back to the problem itself, we use the description of" limited counterexamples ". If we want to solve this problem positively, the only way seems to be to find these two circles constructively in any graph …”

It turns out that someone's soul will shine.

It's so brilliant that people can't move their eyes.

Lingxuan stood beside him, slightly side his head, and this angle can just make the following students can't see the infatuation in his eyes at the moment.

His heart beat again and again. The feeling that he was about to break through his chest made him both panic and excited.

He knew that some things could not be restrained.

For example, I like it.

But he didn't even have the courage to say it.

Jiang Fuyue is too dazzling.

Once he thought he had enough light, but now he found that Jiang Fuyue himself was the light source.

Her excellence made him retreat, and her brilliance eclipsed everyone, including herself.

Want, but dare not, that kind of unreachable entanglement has become a kind of torture.

Ling Xuan hung his eyes ruthlessly and must be patient. He warned himself.

At this time, through the half closed back door of the classroom, a man was also staring at the shining girl on the podium.

Jiang Fuyue: "... But the title also tells us that there are limited Counterexamples in this situation, which almost tells us that the road is impassable. Then we might as well change the angle: prove the lemma, use this lemma to lead to contradictions and realize counter evidence..."

Qingling's voice shows absolute rationality, supported by strong logic.

The man looked and listened, smiling slowly in his eyes.

"Professor Xie?" Zhao Tiejun called softly.

Xie Dingyuan suddenly recovered, but his sight did not take back.

Zhao Tiejun followed the trend and said with a smile: "this is the Mathematical Olympiad class. It's not going to participate in the National League soon. It's training."

Xie Dingyuan qingen.

Director Zhao was very interested in him and couldn't help talking about sex: "the girl speaking on the podium is the first in grade three of senior high school, and also the gold medal and special award winner of iPho and IOI. Both subjects have full marks, and the good seedlings of B and Q..."

Speaking of this, Zhao Tiejun was proud and his chest stood up.

"Really?" Xie Dingyuan answered faintly, giving him a chance to continue.

Sure enough, Zhao Tiejun began to talk——

"The child is particularly excellent. None of the teachers in all subjects praises her intelligence."

Xie Dingyuan: Well, brain melon seeds are really flexible. No matter learning or hating others.

"I get along well with my classmates. I'll give you a lecture when I'm free and sort out the key points. Everyone calls her sister for a month."

Xie Dingyuan: sister? Mingming is still a little girl.

"My sports achievements are also outstanding. I have specialized in high jump and shot put. I often play basketball with my classmates after class."

Xie Dingyuan: classmate? Male or female?

"Some time ago, I published a paper on the main page of PRL journal, the title is... ER! I forgot, it's related to bacterial movement anyway."

Needless to say, Xie Dingyuan knows.

He may be the first person to see the prototype of that paper?

"In short, Jiang Fuyue's all-round development of morality, intelligence, physique and beauty is a particularly excellent student and the light of one China!"

Xie Dingyuan couldn't help nodding. A smile flashed in his eyes, but he listened to what had been said inside——

"... therefore, this lemma is as follows: for any positive real number a and natural number n, it is proved that for a graph with n vertices and (1 + a) n edges, there are cycles with a length less than an, and there are only limited counterexamples..."

Just listening to the sound can make him feel good.

"The only bad thing to say," director Zhao sighed, "is that he is a little stubborn and has a big idea."

"Oh?" Xie Dingyuan raised his eyebrows.

"Some time ago, the escort notices of B and Q universities were sent to the school, saying that she was allowed to choose her major at will. Unexpectedly, the child refused when she said no, and there was no room for turning around. The parents also fooled around with her..."

Zhao Tiejun looked sorry.

That's big B and big q!

It is said that Xu Jing, Meng Zhijian and Yu Wenzhou went crazy in the office that day, sighing and scolding.

What about Jiang Fuyue?

Leng was determined to go her own way, and no one could persuade her back.

Xie Dingyuan heard for the first time: "why did she refuse?"

Zhao Tiejun: "seems to be planning to take the college entrance examination?"

At this point, he is a little proud.

Do students in other schools have the courage to refuse B and Q?

No,

But one of them!

More than one!

Ling Xuan also refused. Good guy, can we get together?

This session is really amazing!

Xie Dingyuan took back his sight and smiled at his lower lip: "let's go, director Zhao."

"Oh, OK, is classmate Zhong's leg almost ready?"

"Yes."

"That's good, that's good. In fact, you don't have to go there in person, just make a phone call, or ask Mr. Zhong to bring a leave cancellation note signed by your parents on the day he returns to school..."

It's better than coming in person?

In fact, Zhao Tiejun doesn't know why this giant Buddha suddenly came.

When the school sent him to pick him up, he was stunned.

Xie Dingyuan stepped forward, and the girl's voice behind him became smaller and smaller——

"Suppose a graph has n vertices and at least (1 + a) n edges, and the lengths of all cycles in the graph are different. It is necessary to construct contradictions when n is large enough to prove that this hypothesis is not true. Then we can operate in this way to find the shortest cycle in the graph..."

Xu Jing came back from a teaching and research meeting and suddenly found that the atmosphere in the class was quite harmonious.

He asked the reason, who knows this group of students are more strict than one.

"?" I'm curious, scratching my heart and lungs.

But he didn't tangle for too long. Harmony is a good thing.

This friendly atmosphere lasted until the end of the two-week semi closed training.

Soon, the Olympic Mathematics National League came