Abstract
For graphs F, G and H, let \(F\rightarrow (G,H)\) signify that any red-blue edge coloring of F contains either a red G or a blue H, hence the Ramsey number R(G, H) is the smallest r such that \(K_r\rightarrow (G,H)\). Define \(K_t\) as the surplus clique of (G, H) if \(K_r\setminus K_t\rightarrow (G,H)\), where \(r=R(G,H)\). For any graph G with \(s(G)=1\), we shall show that the maximum order of surplus clique of \((G, P_n)\) is exactly \(\lceil \frac{n}{2}\rceil \) for large n.
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Li, Y., Li, Y. & Wang, Y. Maximum clique deleted from ramsey graphs of a graph and paths. J Comb Optim 46, 2 (2023). https://doi.org/10.1007/s10878-023-01068-9
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DOI: https://doi.org/10.1007/s10878-023-01068-9