Multiplicities of Eigenvalues and Tree-Width of Graphs

Journal of Combinatorial Theory. Series B

Volumn 74, Issue 2, 1998, Pages 121-146

  Colin De Verdière, Yves ^a  

^a INSTITUT FOURIER   (France)

Author keywords

Graph; Schr dinger operator; Tree width

Indexed keywords

EID: 0000811227     PISSN: 00958956     EISSN: None     Source Type: Journal    
DOI: 10.1006/jctb.1998.1834     Document Type: Article

References (23)

1. Bacher R., Colin de Verdière Y. Multiplicités de valeurs propres et transformations étoile-triangle des graphes. Bull. Soc. Math. France. 123:1995;101-117.
2. Cheng S. Y. Eigenfunctions and nodal sets. Comment. Math. Helv. 51:1976;43-55.
3. Cohen-Tannoudji C., Diu B., Laloë F. Mécanique quantique I. 1977;Hermann, Paris.
4. Colin de Verdière Y. Sur un nouvel invariant des graphes et un critère de planarité J. Combin. Theory Ser. B. 50:1990;11-21.
5. Colin de Verdière Y. A new graph invariant and a criterion for planarity. Graph Structure Theory. Amer. Math. Soc. Colloq. Publ. 147:1991;Amer. Math. Soc. Providence. p. 137-148.
6. Colin de Verdière Y. Réseaux électriques planaires, I. Comment. Math. Helv. 69:1994;351-374.
7. Colin de Verdière Y. Multiplicités de valeurs propres: Laplaciens discrets et laplaciens continus. Rend. Mat. 7. 13:1993;433-460.
8. Y. Colin de Verdière, Spectres des graphes, Institut Fourier, Grenoble, 1995.
9. Y. Colin de Verdière, Discrete magnetic Schrödinger operators and tree-width of graphs, Institut Fourier, Grenoble, 308, 1995.
10. Colin de Verdière Y. Spectre d'opérateurs différentiels sur les graphes. Proceedings, Conference on Random Walks and Discrete Potential Theory. June 1997;Cortona.
11. Colin de Verdière Y., Gitler I., Vertigan D. Réseaux électriques planaires, II. Comment. Math. Helv. 71:1996;144-167.
12. Colin de Verdière Y., Torki N. Opérateur de Schrödinger avec champs magnétiques. Sém. Théor. Spectrale Géom. (Grenoble). 11:1992-1993;9-18.
13. Y. Colin de Verdière, Y. Pan, B. Ycart, Singular limits of Schrödinger operators and Markov processes, J. Operator Theory.
14. Duistermaat J. Fourier Integral Operators. 1996;Birkhäuser, Basel.
15. Guillemin V., Pollack A. Differential Topology. 1974;Prentice-Hall, New York.
16. van der Holst H. A short proof of the planarity characterization of Colin de Verdière. J. Combin. Theory Ser. B. 65:1995;269-272.
17. van der Holst H. Topological and Spectral Graph Characterizations. 1996;Amsterdam University.
18. H. van der Holst, Graphs with magnetic Schrödinger operators of low corank, 1997.
19. Lieb E., Loss M. Fluxes, Laplacians and Kasteleyn's theorem. Duke Math. J. 71:1993;337-363.
20. L. Lovász, A. Schrijver, A Borsuk theorem for antipodal links and a spectral characterization of linklessly embeddable graphs.
21. Nadirashvili N. Berger's Isoperimetric problem and minimal immersions of surfaces. Geom. Funct. Anal. 6:1996;877-897.
22. Robertson N., Seymour P. Graphs minors. III. Planar tree-width. J. Combin. Theory Ser. B. 36:1984;49-64.
23. Robertson N., Seymour P. Graphs minors. IV. Tree-width and well quasi-ordering. J. Combin. Theory Ser. B. 48:1990;227-254.