Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract   The Ramsey number   R  (  G  ,  H  )   has been actively studied for the past 40 years, and it was determined for a large family of pairs   (  G  ,  H  )   of graphs. The Ramsey number of paths was determined very early on, but surprisingly very little is known about the Ramsey number for the pors of paths. The  r -th por     P    n    r     of a path on  n  vertices is obtained by joining any two vertices with distance at most  r .   show that   R  (    P    3  n    2    ,    P    3  n    2    )  =  9  n  −  3   for  n  large and discuss some related questions.
['Peter Allen', 'Barnaby Roberts', 'Jozef Skokan']
I am writing a research paper on a idea Ramsey Numbers of Squares of Paths
[{"from": "human", "value": "I am writing a research paper on a idea Ramsey Numbers of Squares of Paths"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract   The Ramsey number   R  (  G  ,  H  )   has been actively studied for the past 40 years, and it was determined for a large family of pairs   (  G  ,  H  )   of graphs. The Ramsey number of paths was determined very early on, but surprisingly very little is known about the Ramsey number for the pors of paths. The  r -th por     P    n    r     of a path on  n  vertices is obtained by joining any two vertices with distance at most  r .   show that   R  (    P    3  n    2    ,    P    3  n    2    )  =  9  n  \u2212  3   for  n  large and discuss some related questions."}]