拉姆齐图R(4,5)的递阶生成(英文)

A Construction of Ramsey Graph of R(4,5) by the Method of Recursive Generation

对于已知经典的拉姆齐数,其对应的拉姆齐图R(3,3),R(3,4)R(3,5),R(3,6),R(3,7),R(3,8)和R(3,9)均可递阶生成.给出了一个通过R(4,4)图递阶生成的一个R(4,5)拉姆齐图,证明了R(4,5)≥25.同时发现修改所构造的R(4,5)图的10条拉姆齐临界边,该图将变为经典10-正则的R(4,5)图.

For the known classic Ramsey numbers,the Ramsey graphs of R(3,3),R(3,4),R(3,5),R(3,6),R(3,7) and R(3,8) can be constructed by the method of recursive generation.A construction of Ramsey graphs R(4,5) by the method of recursive generation is given and R(4,5)25 is proved.Some critical edges are found in the graph,by changing the color of some critical edges,the Ramsey graph of R(4,5) will turn into a 10-regular symmetric cyclic Ramsey graph of R(4,5).