Discrete Mathematics and Combinatorics Commons^™

Characterizing Sparse Graphs By Map Decompositions, Ruth Haas, Audrey Lee, Ileana Streinu, Louis Theran

Mathematics Sciences: Faculty Publications

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 ℓ edges; (2) the addition of some ℓ edges. These graphs are identified with classes of sparse graphs; the results are also given in matroidal terms.