Balancing Covectors
Laura E. Chávez-Lomelí, Luis Goddyn, Winfried Hochstättler · SIAM Journal on Discrete Mathematics · 2011
Goddyn, Hliněný, and Hochstättler proved that the circular flow number introduced by Goddyn, Tarsi, and Zhang for an oriented matroid of rank [Formula: see text] is bounded by [Formula: see text]. We improve this bound by showing that any oriented matroid without a coloop admits a reorientation such that the imbalance of each covector is at most [Formula: see text]. In particular this yields a new upper bound for the circular flow number.