Lower bounds of Ramsey numbers based on cubic residues
نویسندگان
چکیده
A method to improve the lower bounds for Ramsey numbers R(k; l) is provided: one may construct cyclic graphs by using cubic residues modulo the primes in the form p=6m + 1 to produce desired examples. In particular, we obtain 16 new lower bounds, which are R(6; 12)¿ 230; R(5; 15)¿ 242; R(6; 14)¿ 284; R(6; 15)¿ 374; R(6; 16)¿ 434; R(6; 17)¿ 548; R(6; 18)¿ 614; R(6; 19)¿ 710; R(6; 20)¿ 878; R(6; 21)¿ 884; R(7; 19)¿ 908; R(6; 22)¿ 1070; R(8; 20)¿ 1094; R(7; 21)¿ 1214; R(9; 20)¿ 1304; R(8; 21)¿ 1328: c © 2002 Elsevier Science B.V. All rights reserved.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 250 شماره
صفحات -
تاریخ انتشار 2002