# Characterizing Sparse Graphs by Map Decompositions - Mathematics > Combinatorics

Abstract: A {\bf map} is a graph that admits an orientation of its edges so that eachvertex has out-degree exactly 1. We characterize graphs which admit adecomposition into $k$ edge-disjoint maps after: (1) the addition of {\it any}$\ell$ edges; (2) the addition of {\it some} $\ell$ edges. These graphs areidentified with classes of {\it sparse} graphs; the results are also given inmatroidal terms.

Author: Ruth Haas, Audrey Lee, Ileana Streinu, Louis Theran

Source: https://arxiv.org/