For a set F of finite tournaments, the F-free orientation problem is the problem of orienting a given finite undirected graph in such a way that the resulting oriented graph does not contain any member of F. Using the theory of smooth approximations, we give a new shorter proof of the complexity dichotomy for such problems obtained recently by Bodirsky and Guzm\'{a}n-Pro. In fact, our approach yields a complexity dichotomy for a considerably larger class of computational problems where one is given an undirected graph along with additional local constraints on the allowed orientations. Moreover, the border between tractable and hard problems is described by a decidable algebraic condition.

翻译：对于有限锦标赛集合F，无F定向问题旨在为给定有限无向图寻找一种定向方式，使得所得有向图不包含F中任何成员。基于光滑逼近理论，我们为Bodirsky与Guzmán-Pro近期建立的此类问题复杂性二分定理提供了更简洁的新证明。实际上，我们的方法可推广至更广泛的计算问题类，这类问题在给定无向图的同时还包含关于允许定向的局部约束条件。此外，可解问题与难解问题的分界可由可判定的代数条件精确刻画。