New lower bounds of ten classical Ramsey numbers
نویسندگان
چکیده
Based on a study of basic properties of cyclic graphs of prime order, we give an algorithm for computing lower bounds of classical Ramsey numbers. Our algorithm reduces certain amount of computation of cyclic graphs of prime order, since only some of them normalized cyclic graphs require computation in our method. Using the algorithm, we construct ten cyclic graphs of prime order to obtain new lower bounds of ten classical Ramsey numbers: R(3, 31) 2: 198, R( 4, 17) 2: 182, R(5, 16) 2: 278, R(5, 20) 2: 380, R(5,25) 2: 458, R(7, 15) ~ 444, R(7, 16) 2: 462, R(8, 13) 2: 422, R(8, 15) 2: 618, R(10, 16) 2: 1052.
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عنوان ژورنال:
- Australasian J. Combinatorics
دوره 24 شماره
صفحات -
تاریخ انتشار 2001