Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract   An oriented graph is a directed graph with no cycle of length one or two. The relative clique number of an oriented graph is the order of a largest subset  X  of vertices such that each pair of vertices are either adjacent or connected by a directed 2-path. It is known that the oriented relative clique number of a planar graph is at most 80. Here  improve the upper bound to 50.  also prove an upper bound of 26 for oriented relative clique number of triangle-free planar graphs. Furthermore,  determine the exact values of oriented relative clique number of the families of outerplanar graphs with girth at least g and planar graphs with girth at least   g  +  2   for all   g  ≥  3  .
['Sandip Das', 'Swathyprabhu Mj', 'Sagnik Sen']
I am writing a research paper on a idea On oriented relative clique number
[{"from": "human", "value": "I am writing a research paper on a idea On oriented relative clique number"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract   An oriented graph is a directed graph with no cycle of length one or two. The relative clique number of an oriented graph is the order of a largest subset  X  of vertices such that each pair of vertices are either adjacent or connected by a directed 2-path. It is known that the oriented relative clique number of a planar graph is at most 80. Here  improve the upper bound to 50.  also prove an upper bound of 26 for oriented relative clique number of triangle-free planar graphs. Furthermore,  determine the exact values of oriented relative clique number of the families of outerplanar graphs with girth at least g and planar graphs with girth at least   g  +  2   for all   g  \u2265  3  ."}]