Almost all 5-regular graphs have a 3-flow
Combinatorics
2016-08-08 v2 Probability
Abstract
Tutte conjectured in 1972 that every 4-edge connected graph has a nowhere-zero 3-flow. This has long been known to be equivalent to the conjecture that every 5-regular 4-edge-connected graph has an edge orientation in which every out-degree is either 1 or 4. We show that the assertion of the conjecture holds asymptotically almost surely for random 5-regular graphs. It follows that the conjecture holds for almost all 4-edge connected 5-regular graphs.
Keywords
Cite
@article{arxiv.1503.03572,
title = {Almost all 5-regular graphs have a 3-flow},
author = {Pawel Pralat and Nick Wormald},
journal= {arXiv preprint arXiv:1503.03572},
year = {2016}
}