Báo cáo khoa học:Even circuits of prescribed clockwise parity

We show that a graph has an orientation under which every circuit of even length is clockwise odd if and only if the graph contains no subgraph which is, after the contraction of at most one circuit of odd length, an even subdivision of K2,3. In fact we give a more general characterisation of graphs that have an orientation under which every even circuit has a prescribed clockwise parity. Moreover we show that this characterisation has an equivalent analogue for signed graphs.