On dihedral flows in embedded graphs release_5e76lzrdnfe6vldqr2ix3lioja

by Bart Litjens

Released as a article .

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.
In text/plain format

Archived Files and Locations

application/pdf  237.2 kB
file_kagygw7m7zek7en6qb2erioy2e
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   accepted
Date   2018-12-02
Version   v2
Language   en ?
arXiv  1709.06469v2
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 9f017cb7-03e2-4d80-961f-47b8c45335b8
API URL: JSON