Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: For r ≥ 3, a clique-extension of order r + 1 is a connected graph that consists of a Kr plus another vertex adjacent to at most r − 1 vertices of Kr.   consider the problem of finding the smallest number t such that any graph G of order n admits a decomposition into edge disjoint copies of a fixed graph H and single edges with at most t elements. Here  solve the case when H is a fixed clique-extension of order r + 1, for all r ≥ 3 and will also obtain all extremal graphs. This work extends results proved −
['Teresa Sousa']
I am writing a research paper on a idea Decompositions of graphs into a given clique-extension
[{"from": "human", "value": "I am writing a research paper on a idea Decompositions of graphs into a given clique-extension"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: For r \u2265 3, a clique-extension of order r + 1 is a connected graph that consists of a Kr plus another vertex adjacent to at most r \u2212 1 vertices of Kr.   consider the problem of finding the smallest number t such that any graph G of order n admits a decomposition into edge disjoint copies of a fixed graph H and single edges with at most t elements. Here  solve the case when H is a fixed clique-extension of order r + 1, for all r \u2265 3 and will also obtain all extremal graphs. This work extends results proved \u2212"}]