Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let   G     G        be a graph, and let   S     S        be a subset of the vertex set of   G     G       .  denote the set of the end vertices of a path   P     P        by   end(P)     e  n  d   (  P  )        . A path   P     P        is an   S     S       -path if   |V(P)|≥2     |  V   (  P  )   |  ≥  2        and   V(P)∩S=end(P)     V   (  P  )   ∩  S  =  e  n  d   (  P  )        . An   S     S       -path-system is a graph   H     H        such that   H     H        contains all vertices of   S     S        and every component of   H     H        is an   S     S       -path. ,  give a sharp degree sum condition for a bipartite graph to have a spanning   S     S       -path-system.
['Ryota Matsubara', 'Hajime Matsumura', 'Masao Tsugaki', 'Tomoki Yamashita']
I am writing a research paper on a idea Degree sum conditions for path-factors with specified end vertices in bipartite graphs
[{"from": "human", "value": "I am writing a research paper on a idea Degree sum conditions for path-factors with specified end vertices in bipartite graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let   G     G        be a graph, and let   S     S        be a subset of the vertex set of   G     G       .  denote the set of the end vertices of a path   P     P        by   end(P)     e  n  d   (  P  )        . A path   P     P        is an   S     S       -path if   |V(P)|\u22652     |  V   (  P  )   |  \u2265  2        and   V(P)\u2229S=end(P)     V   (  P  )   \u2229  S  =  e  n  d   (  P  )        . An   S     S       -path-system is a graph   H     H        such that   H     H        contains all vertices of   S     S        and every component of   H     H        is an   S     S       -path. ,  give a sharp degree sum condition for a bipartite graph to have a spanning   S     S       -path-system."}]