Who came up with the four color conjecture? What does the four color conjecture mean

The four-color conjecture was first proposed by Francisguthrie. In 1852, when Guthrie, a graduate of the University of London, came to work on map coloring at a scientific research institute, he discovered that each map could be colored in only four colors. Can this phenomenon be mathematically rigorously proven?

He and his brother, who is in college, decided to give it a try, but there was a huge pile of paper, and no progress was made.

On October 23, 1852, his brother consulted his teacher, the famous mathematician de Morgan, about the proof of the problem, but Morgan could not find a solution to the problem, so he wrote to his friend Sir Hamilton, the famous mathematician, for advice, but the problem was not solved until Hamilton's death in 1865.

In 1872, Kelly, the most famous mathematician in Britain at that time, formally proposed this problem to the London Mathematical Society, so the four-color conjecture became a concern of the world's mathematical community, and many first-class mathematicians in the world participated in the four-color conjecture conference.

The four-color conjecture] The four-color theorem, also known as the four-color conjecture and the four-color problem, is one of the three major mathematical conjectures in the world. The four-color theorem is a well-known mathematical theorem, which is commonly known as the fact that each flat map can be colored with only four colors, and no two adjacent areas are the same color.

In 1976, the four-color problem was proved with the help of an electronic computer, and the problem finally became a theorem, which was the first theorem to be proved with the help of a computer. The essence of the four-color theorem is that it is impossible to construct five or more regions connected by pairs on a plane or sphere.

The four-color theorem, also known as:Four-color conjectureThe four-color problem is one of the three major mathematical conjectures in the world. The essence of the four-color theorem is the intrinsic property of the two-dimensional plane, that is, there can be no two straight lines that cross in the plane and there is no common point in the clump rock. Infiltrate

The four-color question reads, "Any map with just four colors can paint a country with a common border in different colors." In other words, without causing confusion, a map only needs to be marked with four colors.

In mathematical terms, it is "arbitrarily subdivided into non-overlapping regions, each of which can always be marked with one of the four numbers 1234, without giving two adjacent regions the same number." "By adjacent area, we mean that there is an entire section of boundary that is public. If two regions meet only one point or a finite number of points, they are not called adjacent.

Because coloring them with the same color will not cause confusion.

The theoretical basis of the four-color conjecture is as follows:

There must be neighborhoods in any area on the map.

And through the indirect connection between neighborhoods and other non-neighborhoods, any map can be represented as graphically theoretic. Suppose there is a map that requires at least m coloring, then there is only one condition that determines that the map must be colored by m, that is, the map has at least such a region q, and all areas adjacent to this area must meet the m-1 coloring.

Firstly, after satisfying this condition, Q can only use the mth color, and secondly, if the first inference is wrong, for the m coloring map there is no such area, then the neighborhood of any area on the map can only satisfy the coloring less than m-1, then the whole map will not need m colors, which contradicts the assumption, so this is a sufficient and necessary condition.

Suppose we take a map m with at least m coloring of any structure, and there are n regions on it that meet the above conditions, then we can remove all the n regions in the graph theory graph and their relationship lines with neighbors, so that we can transform the problem of constructing a map m with at least m coloring into a region problem that needs to add n regions to at least m-1 coloring map that satisfies the inference one condition.

If the five-coloring map exists and can be constructed successfully, then there must be a four-coloring model map that constructs such a five-coloring model, and to exist such a four-coloring model map, there must be a three-coloring model map that constructs the four-colored, and in the same way, to exist such a three-coloring model map, there must be a two-coloring model map that constructs it, so let's construct whether the five-color map exists.

Hiywood changed the "four-color conjecture" to the "five-color theorem", which was a concession to strengthen the propositional condition.

The four-color theorem (one of the three major mathematical problems in modern times), also known as the four-color conjecture and the four-color problem, is one of the three major mathematical conjectures in the world. The essence of the four-color theorem is the intrinsic property of the two-dimensional plane, that is, two straight lines that cannot cross without a common point in the plane.

Many people have proved that it is impossible to construct five or more two-by-two regions in a two-dimensional plane, but they have not raised them to the level of logical relations and intrinsic properties of two-dimensional, so that many pseudo-counterexamples have appeared.

However, these are precisely the research and development of the rigor of graph theory. Although the computer proved that although it made tens of billions of judgments, it only succeeded in the huge numerical superiority after all, which does not conform to the rigorous logical system of mathematics, and there are still countless mathematics enthusiasts who devote themselves to research.

Heywood conjecture

The Heawood Conjecture is an important conjecture in graph theory j.) was proposed in 1890.

At that time, in order to solve the four-color problem, Heywood established a more general proposition, denoting x(s) as the upper bound of the color numbers of all maps on the surface S, and Heywood conjectured that there was the following formula:

The square brackets indicate the rounding, and the four-color conjecture is exactly the case of e(s)=2, here, the square brackets indicate the whole above the inner number, because, at that time, I don't know whether the four-color conjecture is true, so the case of e=2 is excluded from the formula, and it took nearly a century to study whether this conjecture is true or not, and it was only at the end of the 60s of the 20th century that it was completely solved, and the result is that, except for the Klein bottle n, the only exception to this mill, the Hewood conjecture is true, therefore, The following proven formula is referred to as the Heywood formula, or Heywood's theorem, or the map coloring theorem.

The above content refers to: Encyclopedia-Hewood Conjecture.

Subject, you don't even understand the four-color problem. You don't touch any of the 4 boxes. It can be used in the same color. Only two shapes that touch each other require color inconsistencies.

The four-color conjecture is correct, and this can be proved by a computer, but no one has directly proved him correct so far.

You get it wrong with zz, it's to divide it into n spaces with straight lines, and then color them separately