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.
The strong chromatic index ofK {t, t}-free graphs
2 Pith papers cite this work. Polarity classification is still indexing.
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Online algorithms achieve multiplicative approximation r^{1/(r-1)} for maximum independent sets in dense r-uniform ER hypergraphs and (max γ_i)^{-1/(r-1)} for balanced sets in r-partite versions, with matching lower bounds.
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Algorithmic Phase Transition for Large Independent Sets in Dense Hypergraphs
Online algorithms achieve multiplicative approximation r^{1/(r-1)} for maximum independent sets in dense r-uniform ER hypergraphs and (max γ_i)^{-1/(r-1)} for balanced sets in r-partite versions, with matching lower bounds.