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arXiv · 2609.40018

Separating Notions of Graph Width: the Adaptive, Normal, Linear, Entropic, and Submodular Width

Matthias Lanzinger·Timo Camillo Merkl·Dan Suciu
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Abstract

We describe one explicit simple graph G on 32 vertices whose adaptive, normal, linear, entropic, and submodular widths are pairwise distinct. We compute all these widths exactly, except for the entropic width, where we only give a lower and upper bound. We use Ingleton's inequality and the Zhang-Yeung inequality for upper bounds, and give explicit constructions of modular, normal, linear, entropic, and non-entropic polymatroids for lower bounds.

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Matthias Lanzinger, Timo Camillo Merkl, Dan Suciu. 2026-09-30. Separating Notions of Graph Width: the Adaptive, Normal, Linear, Entropic, and Submodular Width. https://arxiv.org/abs/2609.40018

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