A linear bound for the Colin de Verdiére parameter $μ$ for graphs embedded on surfaces

Camille Lanuel; Francis Lazarus; Rudi Pendavingh

doi:10.48550/arXiv.2303.00556

A linear bound for the Colin de Verdiére parameter $μ$ for graphs embedded on surfaces

Camille Lanuel, Francis Lazarus, Rudi Pendavingh

Combinatorial Optimization

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Abstract

We provide a combinatorial and self-contained proof that for all graphs $G$ embedded on a surface $S$, the Colin de Verdi\`ere parameter $\mu(G)$ is upper bounded by $7-2\chi(S)$.

Original language	English
Article number	2303.00556
Number of pages	9
Journal	arXiv
Volume	2023
DOIs	https://doi.org/10.48550/arXiv.2303.00556
Publication status	Published - 1 Mar 2023

Keywords

math.CO
cs.CG

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10.48550/arXiv.2303.00556

2303.00556v1Final published version, 361 KB

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title = "A linear bound for the Colin de Verdi{\'e}re parameter \$μ\$ for graphs embedded on surfaces",

abstract = "We provide a combinatorial and self-contained proof that for all graphs \$G\$ embedded on a surface \$S\$, the Colin de Verdi\textbackslash{}`ere parameter \$\textbackslash{}mu(G)\$ is upper bounded by \$7-2\textbackslash{}chi(S)\$.",

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AU - Pendavingh, Rudi

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A linear bound for the Colin de Verdiére parameter $μ$ for graphs embedded on surfaces

Abstract

Keywords

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