- A minor-monotone graph parameter based on oriented matroids
- Discrete mathematics
- Pages (from-to)
- Document type
- Faculty of Economics and Business (FEB)
Faculty of Science (FNWI)
- Amsterdam School of Economics Research Institute (ASE-RI)
Korteweg-de Vries Institute for Mathematics (KdVI)
- 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.
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