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