Exponentially Many Nowhere-Zero DOUBLE-STRUCK CAPITAL Z(3)-, DOUBLE-STRUCK CAPITAL Z(4)-, and DOUBLE-STRUCK CAPITAL Z(6)-Flows

摘要

We prove that, in several settings, a graph has exponentially many nowhere-zero flows. These results may be seen as a counting alternative to the well-known proofs of existence of DOUBLE-STRUCK CAPITAL Z(3-), DOUBLE-STRUCK CAPITAL Z(4-), and DOUBLE-STRUCK CAPITAL Z(6)-flows. In the dual setting, proving exponential number of 3-colorings of planar triangle-free graphs is a related open question due to Thomassen.