On dihedral flows in embedded graphs
release_5e76lzrdnfe6vldqr2ix3lioja
by
Bart Litjens
2018
Abstract
Let Γ be a multigraph with for each vertex a cyclic order of the edges
incident with it. For n ≥ 3, let D_2n be the dihedral group of order
2n. Define D := {(< s m a l l m a t r i x >) | a ∈Z}. In [5] it was asked whether
Γ admits a nowhere-identity D_2n-flow if and only if it admits a
nowhere-identity D-flow with |a| < n (a `nowhere-identity
D_n-flow'). We give counterexamples to this statement and provide
general obstructions. Furthermore, the complexity of the existence of
nowhere-identity D_2-flows is discussed. Lastly, graphs in which the
equivalence of the existence of flows as above is true, are described. We focus
particularly on cubic graphs.
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