The doubled edge-stage lift HL'_2(G) produces perfect claw-free box-perfect graphs for any input G, with explicit spectral formulas and gap control in the regular case.
Diestel, Graph Theory, 5th ed., Springer
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A single theorem showing that any efficient k-tangle-distinguishing tree-decomposition of a graph can be refined so each part is either too small for a k-tangle or minimal while containing one.
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Perfecting the Line Graph
The doubled edge-stage lift HL'_2(G) produces perfect claw-free box-perfect graphs for any input G, with explicit spectral formulas and gap control in the regular case.
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Optimal trees of tangles: refining the essential parts
A single theorem showing that any efficient k-tangle-distinguishing tree-decomposition of a graph can be refined so each part is either too small for a k-tangle or minimal while containing one.