Abstract
We present a combinatorial algorithm for the $1$-$(S,T)$-edge-connectivitxy augmentation problem in digraphs. The general $k$-$(S,T)$-edge-connectivity augmentation problem was first solved by A. Frank and T. Jordan, Minimal Edge-coverings by Pairs of Sets, Journal of Combinatorial Theory Ser. B, submitted, but their proof does not yield a polynomial-time algorithm. Our algorithm generalizes an earlier result of P. Eswaran and R. E. Tarjan and relies heavily on the nature of the special case $k = 1$.
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