A linkage of order k of a graph G is a subgraph with k components, each of which is a path. A linkage is vital if it spans all vertices, and no other linkage connects the same pairs of end vertices. We give a characterization of the graphs with a vital linkage of order 2: they are certain minors of a family of highly structured graphs.
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Cornell University Library
arXiv.org e-Print archive
Matroid Structure for Efficiency
Networks and Optimization

Mayhew, D, Whittle, G, & van Zwam, S.H.M. (2010). The structure of graphs with a vital linkage of order 2. arXiv.org e-Print archive. Cornell University Library .