Graphs with magnetic Schrödinger operators of low corank

H. Holst, van der

doi:10.1006/jctb.2001.2087

Graphs with magnetic Schrödinger operators of low corank

H. Holst, van der

Research output: Contribution to journal › Article › Academic › peer-review

13 Citations (Scopus)

Abstract

Colin de Verdière (1998, J. Combin. Theory, Ser. B.74, 121–146) introduced the graph parameter ¿(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, ¿(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 ¿(G)k.

Original language	English
Pages (from-to)	311-339
Journal	Journal of Combinatorial Theory, Series B
Volume	84
Issue number	2
DOIs	https://doi.org/10.1006/jctb.2001.2087
Publication status	Published - 2002

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10.1006/jctb.2001.2087

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title = "Graphs with magnetic Schr{\"o}dinger operators of low corank",

abstract = "Colin de Verdi{\`e}re (1998, J. Combin. Theory, Ser. B.74, 121–146) introduced the graph parameter ¿(G), which is defined as the maximal corank of any positive semidefinite magnetic Schr{\"o}dinger operator fulfilling a certain transversality condition. He showed that for connected simple graphs, ¿(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 ¿(G)k.",

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AB - Colin de Verdière (1998, J. Combin. Theory, Ser. B.74, 121–146) introduced the graph parameter ¿(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, ¿(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 ¿(G)k.

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DO - 10.1006/jctb.2001.2087

M3 - Article

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VL - 84

SP - 311

EP - 339

JO - Journal of Combinatorial Theory, Series B

JF - Journal of Combinatorial Theory, Series B

IS - 2

ER -

Graphs with magnetic Schrödinger operators of low corank

Abstract

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