Abstract
A theorem of Sands, Sauer, and Woodrow, extending the Gale–Shapley theorem, states that if G is a digraph whose arc set is the union of the arc sets of two posets, then G has a kernel. We prove a weighted version of this theorem.
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Aharoni, R., Berger, E. & Gorelik, I. Kernels in Weighted Digraphs. Order 31, 35–43 (2014). https://doi.org/10.1007/s11083-013-9286-4
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DOI: https://doi.org/10.1007/s11083-013-9286-4