Antisymmetric flows in matroids

We present a seemingly new definition of flows and flow numbers for oriented matroids and prove that the flow number L and the antisymmetric flow number Las of an oriented matroid are bounded with its rank. In particular we show that if O is an oriented matroid of rank r then L(O) r + 2 and Las(O) 3 9 2 r +1 . Furthermore, we introduce the notion of a semiflow and show that each oriented matroid has an antisymmetric 3-NZ-semiflow.

• Type: Journal
• Year: 2006
• Where: EJC
• Authors: Winfried Hochstättler, Jaroslav Nesetril
• Keywords: Antisymmetric Flow Number, EJC 2006, EJC 2007, Flow Number, Oriented Matroid