Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A Disjoint Path Cover (DPC for short) of a graph is a set of pairwise (internally) disjoint paths that altogether cover every vertex of the graph. Given a set S of k sources and a set T of k sinks, a many-to-many k-DPC beten S and T is a disjoint path cover each of whose paths joins a pair of source and sink. It is classied as paired if each source of S must be joined to a designated sink ofT , or unpaired if there is no such constraint. ,  show that every m-dimensional restricted hypercube-like graph with at most m 3 faulty vertices and/or edges being removed has a paired (and unpaired) 2-DPC joining arbitrary two sources and two sinks where m 5. The bound m 3 on the number of faults is optimal for both paired and unpaired types.
['Sook-Yeon Kim', 'Jung-Heum Park']
I am writing a research paper on a idea Many-to-many two-disjoint path covers in restricted hypercube-like graphs
[{"from": "human", "value": "I am writing a research paper on a idea Many-to-many two-disjoint path covers in restricted hypercube-like 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 Disjoint Path Cover (DPC for short) of a graph is a set of pairwise (internally) disjoint paths that altogether cover every vertex of the graph. Given a set S of k sources and a set T of k sinks, a many-to-many k-DPC beten S and T is a disjoint path cover each of whose paths joins a pair of source and sink. It is classied as paired if each source of S must be joined to a designated sink ofT , or unpaired if there is no such constraint. ,  show that every m-dimensional restricted hypercube-like graph with at most m 3 faulty vertices and/or edges being removed has a paired (and unpaired) 2-DPC joining arbitrary two sources and two sinks where m 5. The bound m 3 on the number of faults is optimal for both paired and unpaired types."}]