Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777365 | European Journal of Combinatorics | 2017 | 8 Pages |
Abstract
We transfer Tutte's theory for analyzing the chromatic number of a graph using nowhere-zero-coflows and -flows (NZ-flows) to the dichromatic number of a digraph and define Neumann-Lara-flows (NL-flows). We prove that any digraph whose underlying (multi-)graph is 3-edge-connected admits a NL-3-flow, and even a NL-2-flow in case the underlying graph is 4-edge connected. We conjecture that 3-edge-connectivity already guarantees the existence of a NL-2-flow, which, if true, would imply the 2-Color-Conjecture for planar graphs due to VÃctor Neumann-Lara. Finally we present an extension of the theory to oriented matroids.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Winfried Hochstättler,