Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A many-to-many k -disjoint path cover of a graph joining two disjoint vertex subsets S and T of equal size k is a set of k vertex-disjoint paths beten S and T that altogether cover every vertex of the graph. It is classified as paired if each source in S is required to be paired with a specific sink in T , or unpaired otherwise. ,  develop Ore-type sufficient conditions for the existence of many-to-many k -disjoint path covers joining arbitrary vertex subsets S and T . Also, an Ore-type degree condition is established for the one-to-many k -disjoint path cover, a variant derived by allowing to share a single source. The bounds on the degree sum are all best possible.
['Hyeong-Seok Lim', 'Hee-Chul Kim', 'Jung-Heum Park']
I am writing a research paper on a idea Ore-type degree conditions for disjoint path covers in simple graphs
[{"from": "human", "value": "I am writing a research paper on a idea Ore-type degree conditions for disjoint path covers in simple graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A many-to-many k -disjoint path cover of a graph joining two disjoint vertex subsets S and T of equal size k is a set of k vertex-disjoint paths beten S and T that altogether cover every vertex of the graph. It is classified as paired if each source in S is required to be paired with a specific sink in T , or unpaired otherwise. ,  develop Ore-type sufficient conditions for the existence of many-to-many k -disjoint path covers joining arbitrary vertex subsets S and T . Also, an Ore-type degree condition is established for the one-to-many k -disjoint path cover, a variant derived by allowing to share a single source. The bounds on the degree sum are all best possible."}]