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arXiv · 0704.3843

Characterizing Sparse Graphs by Map Decompositions

Ruth Haas·Audrey Lee·Ileana Streinu·Louis Theran
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Abstract

A {\bf 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 {\it any} $\ell$ edges; (2) the addition of {\it some} $\ell$ edges. These graphs are identified with classes of {\it sparse} graphs; the results are also given in matroidal terms.

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Ruth Haas, Audrey Lee, Ileana Streinu, Louis Theran. 2007-04-29. Characterizing Sparse Graphs by Map Decompositions. https://arxiv.org/abs/0704.3843

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