Preserving and Increasing Local Edge-Connectivity in Mixed Graphs
- 1 May 1995
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Discrete Mathematics
- Vol. 8 (2) , 155-178
- https://doi.org/10.1137/s0036142993226983
Abstract
Generalizing and unifying earlier results of W. Mader, and A. Frank and B. Jackson, we prove two splitting theorems concerning mixed graphs. By invoking these theorems we obtain min-max formulae for the minimum number of new edges to be added to a mixed graph so that the resulting graph satisfies local edge-connectivity prescriptions. An extension of Edmonds's theorem on disjoint arborescences is also deduced along with a new sufficient condition for the solvability of the edge-disjoint paths problem in digraphs. The approach gives rise to strongly polynomial algorithms for the corresponding optimization problems.Keywords
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