CoEulerian graphs
Abstract
We suggest a measure of "Eulerianness" of a finite directed graph and define a class of "coEulerian" graphs. These are the graphs whose Laplacian lattice is as large as possible. As an application, we address a question in chip-firing posed by Bjorner, Lovasz, and Shor in 1991, who asked for "a characterization of those digraphs and initial chip configurations that guarantee finite termination." Bjorner and Lovasz gave an exponential time algorithm in 1992. We show that this can be improved to linear time if the graph is coEulerian, and that the problem is NP-complete for general directed multigraphs.
Keywords
Cite
@article{arxiv.1502.04690,
title = {CoEulerian graphs},
author = {Matthew Farrell and Lionel Levine},
journal= {arXiv preprint arXiv:1502.04690},
year = {2015}
}
Comments
15 pages, to appear in Proc AMS. Main changes in v3: Removed the section on multi-Eulerian tours, which will appear separately. Added Prop 2.13 on graphs that are both Eulerian and coEulerian. Added Table 3.1 on computational complexity