# Characterizing sparse graphs by map decompositions

 Authors: Ruth Haas, Audrey Lee, Ileana Streinu, and Louis Theran Journal: Journal of Combinatorial Mathematics and Combinatorial Computing, 62, 2007. Full text: arXiv

A map is a graph that admits an orientation of its edges so that each vertex has out-degree exactly 1. We characterize graphs which admit a decomposition into $k$ edge-disjoint maps after: (1) the addition of any $\ell$ edges; (2) the addition of some $\ell$ edges. These graphs are identified with classes of sparse graphs; the results are also given in matroidal terms.