Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  give a computer-assisted proof of the fact that $R(K_5-P_3, K_5)=25$. This solves one of the three remaining open cases in Hendry's table, which listed the Ramsey numbers for pairs of graphs on 5 vertices.  find that there exist no $(K_5-P_3,K_5)$-good graphs containing a $K_4$ on 23 or 24 vertices, where a graph $F$ is $(G,H)$-good if $F$ does not contain $G$ and the complement of $F$ does not contain $H$. The unique $(K_5-P_3,K_5)$-good graph containing a $K_4$ on 22 vertices is presented.
['Jesse A. Calvert', 'Michael J. Schuster', 'Stanislaw Radziszowski']
I am writing a research paper on a idea Computing the Ramsey Number $R(K_5-P_3,K_5)$
[{"from": "human", "value": "I am writing a research paper on a idea Computing the Ramsey Number $R(K_5-P_3,K_5)$"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  give a computer-assisted proof of the fact that $R(K_5-P_3, K_5)=25$. This solves one of the three remaining open cases in Hendry's table, which listed the Ramsey numbers for pairs of graphs on 5 vertices.  find that there exist no $(K_5-P_3,K_5)$-good graphs containing a $K_4$ on 23 or 24 vertices, where a graph $F$ is $(G,H)$-good if $F$ does not contain $G$ and the complement of $F$ does not contain $H$. The unique $(K_5-P_3,K_5)$-good graph containing a $K_4$ on 22 vertices is presented."}]