Constant-factor LP-based approximation for Max Dist-2 Independent Set (and Min Dominating Set) in bounded radius-2 merge-width graphs, with the domination-to-2-independence ratio shown bounded and tight for radius-1.
χ-Boundedness and Neighbourhood Complexity of Bounded Merge-Width Graphs
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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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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.