Changes
Stable flows in networks with preferences were introduced by Fleiner <ref name="Fl">T. Fleiner, ''On stable matchings and flows'', [http://www.cs.elte.hu/egres/tr/egres-09-11.pdf EGRES Technical Report no. 2009-11].</ref>.
==Network with preferences==
Each arc has unit capacity, and the preferences are indicated by the numbers around the vertices. Since no arc leaves the set ''{a,b,c}'', no arc entering it can have positive flow, in particular ''sa'' has zero flow. In a strongly stable flow, the cycle ''abc'' must be saturated, but then ''sa'' is a blocking path, a contradiction.
==Generalizations==
Király and Pap <ref name="KiPa"/> generalized the model to '''stable multicommodity flows'''. They showed that there always exists a stable (fractional) multicommodity flow, but, contrary to the stable flow problem, it is PPAD-complete to find one.
==References==
<references> <ref name="Fl">T. Fleiner, ''On stable matchings and flows'', [http://www.cs.elte.hu/egres/tr/egres-09-11.pdf EGRES Technical Report no. 2009-11].</ref> <ref name="KiPa">T. Király, J. Pap, ''Stable multicommodity flows'', [http://www.cs.elte.hu/egres/tr/egres-12-13.pdf EGRES Technical Report no. 2012-13].</ref>
</references>
[[Category: Definitions]]
