This study examines an asset-selection method that combines network theory with a greedy algorithm. We construct a Planar Maximally Filtered Graph (PMFG) from the correlation matrix and select low-correlation assets using the Farthest-First (FF) algorithm based on graph-theoretic shortest-path distances. Using 11 U.S. sector ETFs over 2014–2024, we conduct rolling out-of-sample backtests and compare PMFG-FF against six benchmarks. The main contribution lies in the empirical validation of a two-stage framework (PMFG-MVO) that separates asset selection from weight determination. Within the present setting, PMFG-FF functions as a systematic rule specialized for low-correlation asset selection and exhibits near-optimal performance close to that obtained by exhaustive enumeration. Meanwhile, a tendency that correlation reduction is not accompanied by improvement in risk metrics was observed under the present sample, and this is confined to an empirical observation. We confirm that PMFG-MVO can combine low-correlation maintenance with risk control. This study is an exploratory investigation based on a limited universe, and revalidation on larger asset universes remains future work.