Abstract : Adapting the method introduced in Graph Minors X, we propose a new proof of the duality between the bramble number of a graph and its tree-width. Our approach is based on a new definition of submodularity on partition functions which naturally extends the usual one on set functions. The proof does not rely on Menger's theorem, and thus generalises the original one. It thus provides a dual for matroid tree-width. One can also derive all known dual notions of other classical width-parameters from it.
https://hal-lirmm.ccsd.cnrs.fr/lirmm-00432698
Contributeur : Stephan Thomasse
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Soumis le : mardi 31 août 2010 - 15:10:03
Dernière modification le : jeudi 7 février 2019 - 14:51:34
Document(s) archivé(s) le : mercredi 1 décembre 2010 - 02:26:32
