Abstract
For graphs G and H , the Ramsey number R ( G , H ) is the smallest positive integer n such that every graph F of order n contains G or the complement of F contains H . For the path P n and the wheel W m , it is proved that R ( P n , W m ) = 2 n - 1 if m is even, m ⩾ 4 , and n ⩾ ( m / 2 ) ( m - 2 ) , and R ( P n , W m ) = 3 n - 2 if m is odd, m ⩾ 5 , and n ⩾ ( m - 1 / 2 ) ( m - 3 ) .
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