Even Bonds of Prescribed Directed Parity
Sven Hartmann, Charles H. C. Little · The Electronic Journal of Combinatorics · 2005
Given a set $S$ of vertices in a graph, the cocycle determined by $S$ is the set of edges joining a vertex in $S$ to a vertex not in $S$. A bond is a minimal non-empty cocycle. We characterise graphs that admit an orientation under which every bond of even cardinality has a prescribed directed parity.