The classic combinatorial construct of maximum matchings probes the random geometry of regions with local sublattice imbalance in a site-diluted bipartite lattice. We demonstrate that these regions. which host the monomers of any maximum matching of the lattice. control the localization properties of a zero-energy quantum particle hopping on this lattice. https://allfixelectricales.shop/product-category/fridge-hose-seal/