Characterizing Sparse Graphs by Map Decompositions
Abstract
A {\bf map} is a graph that admits an orientation of its edges so that each vertex has outdegree exactly 1. We characterize graphs which admit a decomposition into $k$ edgedisjoint 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2007
 DOI:
 10.48550/arXiv.0704.3843
 arXiv:
 arXiv:0704.3843
 Bibcode:
 2007arXiv0704.3843H
 Keywords:

 Mathematics  Combinatorics;
 68R10;
 05B35
 EPrint:
 Characterizing sparse graphs by map decompositions. J. Combin. Math. Combin. Comput. 62 (2007), 311