2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114185We give a simple proof of MacLane's algebraic planarity criterion for graphs. This proof does not use any other known planarity criteria. Keywords: graph, planarity, cycle space, a simple basis of a graph.4 pagesCombinatorics05C10Simple and Direct Proof of MacLane's Planarity Criteriontext