Conjecture about the minimum number of VC numbers

[Note in advance that the actual physical link of the actual virtual circuit may have multiple VC numbers at the same time, but eachSegmentThe logical link has only one VC number, and a complete virtual path consists of multipleSegmentComposition]

Problem description:

In a virtual circuit switching network, each direct connection link of a vro has a unique VC number, that is, the link VC numbers connected to the same vro do not conflict. It is known that a vro in the entire network has a maximum of M direct connections, but the number of routers is unknown. How many types of VC numbers are used at least when all possible conditions are considered?

(You can know that the upper limit of the minimum number of VC numbers is required for all possible networking scenarios)

First give a simple answer (guess )? 2s-1

In addition, full-link scenarios are as follows:

There is no clear conclusion yet, but it is noted that the degree of uniformity of dyeing has an important impact on the number of colors used,

For a full-link network composed of N nodes, a total of N (N-1)/two sides need to be stained,

ToSix nodesFor example, a total of 15 edges, because one edge links two nodes,

One color can dye up to three edges (one edge links two points, and the points of edge links of the same color cannot be repeated ),

At least five colors are required, and at least five colors are required.

However, during the attempt, we found the frequency of using the distribution style (5 in total) of the lines painted in the same color on the two-dimensional plane,

Results also have an important impact (in fact, there should be no so-called style problems in the dyeing problem,

Because dyeing ignores dimensions, and each node is completely equal,

In fact, style problems in two dimensions may affect some irrelevant dimensions. The extraction and abstraction of these problems are the purpose of studying the so-called style problems)

Make the entire network color as even as possible (this uniform is unrelated to the uniform dimension, the two-dimensional plane looks even,

There may be non-uniformity in the case of ignoring the dimension) can make the use of as few colors as possible

(17 edges need to be colored, while 4, 4, 4, and 5 edges are evenly distributed in four colors)

Conjecture about the minimum number of VC numbers