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Colorability and realizability defects in resource-dominated packing relaxations

Juan Pablo Traverso Gianini

Palomar Registrypalomar/PALOMAR-2026-11-01-000020Nov 1, 2026math.COscore 0

A Lean 4 / Mathlib formalization of the main results of the author's preprint "Colorability and Realizability Defects in Resource-Dominated Packing Relaxations" (Erdős #81 series, Paper V). For a conflict system (finite objects with a symmetric irreflexive conflict relation) and a multiset X of objects, the loss between fractional and integral packings is bounded by the colourability defect D_q of the conflict graph H[X] of the copies (Lemma 3.1, Corollary 3.2, Theorems 3.3, 3.4, 3.4w), and, more generally, by the cost of a realizability certificate whose classes are realized in a fixed…

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