Graphs with magnetic Schrödinger operators of low corank

Authors:
Hein van der Holst
Affiliations:
Freie Universität Berlin, Fachbereich Mathematik und Informatik, Institute für Mathematik, Arnimallee 2-6, D-14195 Berlin, Germany
Venue:
Journal of Combinatorial Theory Series B
Year:
2002

Citing 3
Cited 1

Graph minors. XIII: the disjoint paths problem

Journal of Combinatorial Theory Series B
Multiplicities of eigenvalues and tree-width of graphs

Journal of Combinatorial Theory Series B
Graph Theory With Applications

Graph Theory With Applications

Some connectivity properties for excluded minors of the graph invariant v(G)

European Journal of Combinatorics

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Abstract

Colin de Verdière (1998, J. Combin. Theory, Ser. B. 74, 121-146) introduced the graph parameter v(G), which is defined as the maximal corank of any positive semidefinite magnetic Schrödinger operator fulfilling a certain transversality condition. He showed that for connected simple graphs, v(G) ≤ 1 if and only if G is a tree. In this paper we characterize for k = 2, 3, the classes of graphs G with v(G) ≤ k.