Paths , Cycles and Wheels sin Graphs without

For any graph F , V (F ) and E (F ) will denote the vertex and edge sets of the p graph F , also let n (F ) = | V (F ) | and e (F ) = | E (F ) | . The graph F  denotes the com lement of F . A graph F will be called a (G , H )−good graph, if F does not contain a ( G and F  does not contain H . Any (G , H )-good graph on n vertices will be called G , H , n )−good graph. The Ramsey number R (G , H ) is defined as the smallest l g integer n such that no (G , H , n )-good graph exists. Any graph is called a critica raph for the Ramsey number R (G , H ) if it is (G , H , R (G , H ) − 1)-good. When the s graph F is fixed, then for any vertex x ∈V (F ), G and H will denote the graph x x , r induced by the neighbors of the vertex x or by all the vertices disconnected from x espectively. P is a path on i vertices, C is a cycle of length i , and W is a wheel w i i i ith i −1 spokes, i.e. a graph formed by some vertex x , called a hub of the wheel, connected to all vertices of some cycle C , called a rim . 2K is the graph formed by i −1 i