Deterministic families of n-vertex graphs achieve provably maximum rank-width Θ(n) via edge-isoperimetric inequalities, strong chromatic index, and a logarithmic strengthening from Boolean analysis.
Preparing graph states forbidding a vertex-minor
2 Pith papers cite this work. Polarity classification is still indexing.
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Graphs admitting Welzl orders with sublinear-interval neighborhoods have small biclique decompositions, yielding log-factor extensions to bounds on Zarankiewicz, matrix multiplication, quantum circuits, and structured shortest paths.
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Entanglement from Expansion: High Rank-Width in Deterministic Graphs
Deterministic families of n-vertex graphs achieve provably maximum rank-width Θ(n) via edge-isoperimetric inequalities, strong chromatic index, and a logarithmic strengthening from Boolean analysis.
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Biclique decompositions from Welzl orders
Graphs admitting Welzl orders with sublinear-interval neighborhoods have small biclique decompositions, yielding log-factor extensions to bounds on Zarankiewicz, matrix multiplication, quantum circuits, and structured shortest paths.