A Linear Bound for the Colin de Verdière Parameter \(\boldsymbol{\mu }\) for Graphs Embedded on Surfaces

We provide a combinatorial and self-contained proof of a result following from G. Besson [Ann. Inst. Fourier, 30 (1980), pp. 109-128] and Y. Colin de Verdiere [Ann. Sci. Ec. Norm. Super., 20 (1987), pp. 599-615] that for all graphs G embedded on a surface S, the Colin de Verdiere parameter μG is upper bounded by 7 2\chi (S).

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Publication Details

Journal
SIAM Journal on Discrete Mathematics
Published
2024-08-12
DOI
https://doi.org/10.1137/23m1623628
Primary Topic
Spectral Theory in Mathematical Physics
Type
article
Field-Weighted Citation Impact
0.00

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article

A Linear Bound for the Colin de Verdière Parameter \(\boldsymbol{\mu }\) for Graphs Embedded on Surfaces

Rudi Pendavingh, Francis Lazarus, Camille Lanuel
SIAM Journal on Discrete Mathematics
Spectral Theory in Mathematical Physics
article

A Linear Bound for the Colin de Verdière Parameter \(\boldsymbol{\mu }\) for Graphs Embedded on Surfaces

Rudi Pendavingh, Francis Lazarus, Camille Lanuel
article en

Abstract

We provide a combinatorial and self-contained proof of a result following from G. Besson [Ann. Inst. Fourier, 30 (1980), pp. 109-128] and Y. Colin de Verdiere [Ann. Sci. Ec. Norm. Super., 20 (1987), pp. 599-615] that for all graphs G embedded on a surface S, the Colin de Verdiere parameter μG is upper bounded by 7 2\chi (S).

SIAM Journal on Discrete MathematicsVol. 38(3)
Centre National de la Recherche Scientifique (FR), Laboratoire des Sciences pour la Conception, l'Optimisation et la Production (FR), Laboratoire Lorrain de Recherche en Informatique et ses Applications (FR), Eindhoven University of Technology (NL), Université Grenoble Alpes (FR), Université de Lorraine (FR)
Agence Nationale de la Recherche
Openalex Percentile: Top 77%
Spectral Theory in Mathematical Physics
DOIOpen Access PDFOpenAlex
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A Linear Bound for the Colin de Verdière Parameter \(\boldsymbol{\mu }\) for Graphs Embedded on Surfaces — Rudi Pendavingh, Francis Lazarus, et al. · SIAM Journal on Discrete Mathematics (2024) | TGRS Research Map | TGRS