  It is known that every multigraph with an even number of edges has an even
orientation (i.e., all indegrees are even). We study parity constrained graph
orientations under additional constraints. We consider two types of constraints
for a multigraph G=(V,E): (1) an exact conflict constraint is an edge set C in
E and a vertex v in V such that C should not equal the set of incoming edges at
v; (2) a subset conflict constraint is an edge set C in E and a vertex v in V
such that C should not be a subset of incoming edges at v. We show that it is
NP-complete to decide whether G has an even orientation with exact or subset
conflicts, for all conflict sets of size two or higher. We present efficient
algorithms for computing parity constrained orientations with disjoint exact or
subset conflict pairs.
