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A king graph \( KG_n \) has \( n^2 \) vertices corresponding to the \( n^2 \) squares of an \( n \times n \) chessboard. From one square (vertex) there are edges to all squares (vertices) being attacked by a king. For given graphs \( G \) and \( H \), the Ramsey number \( r(G, H) \) is the smallest \( n \) such that any 2-coloring of the edges of \( KG_n \) contains \( G \) in the first or \( H \) in the second color. Results on existence and nonexistence of \( r(G, H) \) and some exact values are presented.