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A note on constructive methods for ramsey numbers
Author(s) -
Chung F. R. K.
Publication year - 1981
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190050109
Subject(s) - combinatorics , mathematics , ramsey's theorem , complement (music) , graph , constructive , upper and lower bounds , integer (computer science) , constant (computer programming) , discrete mathematics , mathematical analysis , biochemistry , chemistry , process (computing) , complementation , computer science , programming language , gene , phenotype , operating system
Let r(k ) denote the least integer n ‐such that for any graph G on n vertices either G or its complement G contains a complete graph K k on k vertices. in this paper, we prove the following lower bound for the Ramsey number r(k ) by explicit construction: r(k ) ≥ exp ( c (Log k ) 4/3 [(log log k ) 1/3 ] for some constant c > 0.