The 4-Sample Theorem on planar graphs

Oberwolfach'tan

The 4-Sample Theorem on planar graphs

The famous 4-Color Theorem from graph theory states that the vertices of any planar graph can be colored with four colors, so that no neighboring vertices have the same color. The 4-Sample Theorem from algebraic statistics says that the maximum likelihood estimator for a Gaussian graphical model of a planar graph exists with probability 1 if one has at least four samples. This number of necessary samples, the maximum likelihood threshold, is a new graph invariant from algebraic statistics and connected not only to parameter estimation, but also to matrix completion, the theory of filling partial matrices, and rigidity theory, which deals with stability of objects. 

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Matematiksel konular

Ayrık Matematik ve Matematiğin Temelleri
Olasılık Kuramı ve İstatistik

Yazar(lar)

Carlos Améndola, Thomas Kahle

Lisans

DOI (Dijital nesne belirteci)

10.14760/SNAP-2026-005-EN

PDF indir

snapshot-2026-005.pdf

PDF

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Cebir ve Sayılar Kuramı
Analiz
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Nümerik ve Hesap Analizi
Olasılık Kuramı ve İstatistik

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