English

Checking the admissibility of odd-vertex pairings is hard

Combinatorics 2022-06-15 v2 Discrete Mathematics

Abstract

Nash-Williams proved that every graph has a well-balanced orientation. A key ingredient in his proof is admissible odd-vertex pairings. We show that for two slightly different definitions of admissible odd-vertex pairings, deciding whether a given odd-vertex pairing is admissible is co-NP-complete. This resolves a question of Frank. We also show that deciding whether a given graph has an orientation that satisfies arbitrary local arc-connectivity requirements is NP-complete.

Keywords

Cite

@article{arxiv.2103.00306,
  title  = {Checking the admissibility of odd-vertex pairings is hard},
  author = {Florian Hörsch},
  journal= {arXiv preprint arXiv:2103.00306},
  year   = {2022}
}