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.
Chv´ atal,A characterization of perfect graphs , Journal of Combinatorial Theory, Series B, 13(1):95–98
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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.