Characterizing Sparse Graphs by Map Decompositions

Details Characterizing Sparse Graphs by Map Decompositions Characterizing Sparse Graphs by Map Decompositions

2007-04-29

arxiv.org/abs/0704.3843v1

Characterizing sparse graphs by map decompositions. J. Combin. Math. Combin. Comput. 62 (2007), 3--11

Mathematics

Combinatorics

Scientific paper

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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