A minor-monotone graph parameter based on oriented matroids

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Authors
Publication date 1997
Journal Discrete mathematics
Volume | Issue number 165-166
Pages (from-to) 219-226
Organisations
  • Faculty of Economics and Business (FEB) - Amsterdam School of Economics Research Institute (ASE-RI)
  • Faculty of Science (FNWI) - Korteweg-de Vries Institute for Mathematics (KdVI)
Abstract For an undirected graph G = (V,E) let λ ′(G) be the largest d for which there exists an oriented matroid M on V of corank d such that for each nonzero vector (x+,x−) of M, x+ is nonempty and induces a connected subgraph of G.

We show that λ′(G) is monotone under taking minors and clique sums. Moreover, we show that λ′(G) ≤ 3 if and only if G has no K5- or V8-minor; that is, if and only if G arises from planar graphs by taking clique sums and subgraphs.
Document type Article
Language English
Published at https://doi.org/10.1016/S0012-365X(96)00172-0
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