English

The Merino-Welsh Conjecture holds for Series-Parallel Graphs

Combinatorics 2013-03-27 v1

Abstract

The Merino-Welsh conjecture asserts that the number of spanning trees of a graph is no greater than the maximum of the numbers of totally cyclic orientations and acyclic orientations of that graph. We prove this conjecture for the class of series-parallel graphs.

Keywords

Cite

@article{arxiv.1303.6416,
  title  = {The Merino-Welsh Conjecture holds for Series-Parallel Graphs},
  author = {Steven D. Noble and Gordon F. Royle},
  journal= {arXiv preprint arXiv:1303.6416},
  year   = {2013}
}

Comments

12 pages, includes Mathematica code in Appendix

R2 v1 2026-06-21T23:48:17.342Z