Changes

S. Iwata, T. Király, Z. Király, Z. Szigeti,'' On well-balanced orientations,counter-examples for relatedproblems'' [http://www.cs.elte.hu/egres/www/tr-04-16.html EGRESTechnical Report no. 2004-16].]</ref> that the natural cut inequalities do not describe this polyhedron and it was shown in <ref name="TR-2006-05">A. Bernáth,''Hardness results for well-balanced orientations''[http://www.cs.elte.hu/egres/www/tr-06-05.html EGRES TechnicalReport no. 2006-05.]</ref> that optimization over this polyhedron is NP-hard. In <ref name="TR-2006-05"/> many related problems were shown to be NP-complete, for example the problem introduced here is <math>NP</math>-complete, if we also fix some other odd-degree nodes where we want the in-degree to be more than the out-degree. See also <ref>Z. Király, Z. Szigeti, ''Notes on well-balancedorientations'' ]http://www.cs.elte.hu/egres/www/tr-04-10.html EGRES Technical Report no. 2004-10.]</ref> and <ref>A. Bernáth and G. Joret. ''Well-balanced orientations of mixed graphs'' Inf. Process. Lett., 106(4):149-151, 2008. (See the EGRES Quick Proof version QP-2007-01 at www.cs.elte.hu/egres.)</ref>