The lower bounds for any R（l<sub>1</sub>,…,l<sub>q</sub>;r）are investigated.Let K<sub>n</sub><sup>r</sup> be the completer-uniform hypergraph on n points.Define R（l&...The lower bounds for any R（l<sub>1</sub>,…,l<sub>q</sub>;r）are investigated.Let K<sub>n</sub><sup>r</sup> be the completer-uniform hypergraph on n points.Define R（l<sub>1</sub>,…,l<sub>q</sub>;r）as the minimal natural number n sothat if the edges of K<sub>n</sub><sup>r</sup> are q-colored,there is a set S of l<sub>i</sub>（i∈{1,…,q}）vertices such that alledges on S are of the i-th color.For the special case of q=r=2,the lower bounds were got byP.Erd（?）s and J.Spencer.In this paper,we shall give the lower bounds for any R（l<sub>1</sub>,…,l<sub>q</sub>;r）.展开更多
Three new cyclic graphs are constructed by using a computer, and the lower bounds of three Ramsey numbers obtained: R(6,12)≥224, R(6,14)≥258,R(6,15)≥338, which fill in three blanks in the table of bounds of Ramsey ...Three new cyclic graphs are constructed by using a computer, and the lower bounds of three Ramsey numbers obtained: R(6,12)≥224, R(6,14)≥258,R(6,15)≥338, which fill in three blanks in the table of bounds of Ramsey numbers.展开更多
IT is very difficult to establish the Ramsey number, so we often use the way of getting the up-per and lower bound of the Ramsey number to near the exact value. All lower bounds of R (5,l) known so far are shown in ta...IT is very difficult to establish the Ramsey number, so we often use the way of getting the up-per and lower bound of the Ramsey number to near the exact value. All lower bounds of R (5,l) known so far are shown in table 1.展开更多
文摘The lower bounds for any R（l<sub>1</sub>,…,l<sub>q</sub>;r）are investigated.Let K<sub>n</sub><sup>r</sup> be the completer-uniform hypergraph on n points.Define R（l<sub>1</sub>,…,l<sub>q</sub>;r）as the minimal natural number n sothat if the edges of K<sub>n</sub><sup>r</sup> are q-colored,there is a set S of l<sub>i</sub>（i∈{1,…,q}）vertices such that alledges on S are of the i-th color.For the special case of q=r=2,the lower bounds were got byP.Erd（?）s and J.Spencer.In this paper,we shall give the lower bounds for any R（l<sub>1</sub>,…,l<sub>q</sub>;r）.
文摘Three new cyclic graphs are constructed by using a computer, and the lower bounds of three Ramsey numbers obtained: R(6,12)≥224, R(6,14)≥258,R(6,15)≥338, which fill in three blanks in the table of bounds of Ramsey numbers.
文摘IT is very difficult to establish the Ramsey number, so we often use the way of getting the up-per and lower bound of the Ramsey number to near the exact value. All lower bounds of R (5,l) known so far are shown in table 1.
