English

Multi-Eulerian tours of directed graphs

Combinatorics 2015-09-22 v1

Abstract

Not every graph has an Eulerian tour. But every finite, strongly connected graph has a multi-Eulerian tour, which we define as a closed path that uses each directed edge at least once, and uses edges e and f the same number of times whenever tail(e)=tail(f). This definition leads to a simple generalization of the BEST Theorem. We then show that the minimal length of a multi-Eulerian tour is bounded in terms of the Pham index, a measure of 'Eulerianness'.

Keywords

Cite

@article{arxiv.1509.06237,
  title  = {Multi-Eulerian tours of directed graphs},
  author = {Matthew Farrell and Lionel Levine},
  journal= {arXiv preprint arXiv:1509.06237},
  year   = {2015}
}

Comments

4 pages. Supersedes section 3 of arXiv:1502.04690v2

R2 v1 2026-06-22T11:01:39.088Z