EULERIAN AND BIPARTITE ORIENTABLE MATROIDS
This chapter focuses on extending the characterizations of Eulerian graphs via orientations. An Eulerian tour of a graph G induces an orientation with the property that every cocircuit (minimal edge cut) in G is traversed an equal number of times in each direction. In this sense, the orientation can be considered balanced. Applying duality to planar graphs, these notions produce characterizations of bipartite graphs. These notions are further extended to oriented matroids.
Keywords: Eulerian graphs, orientations, oriented matroids, bipartite graphs
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