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.
Kanj, Michael Pelsmajer, Marcus Schaefer, and Ge Xia
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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.