We investigate the supereulerian graph problems within planar graphs, and we prove that if a \(2\)-edge-connected planar graph \(G\) is at most three edges short of having two edge-disjoint spanning trees, then \(G\) is supereulerian except for a few classes of graphs. This is applied to show the existence of spanning Eulerian subgraphs in planar graphs with small edge cut conditions. We also determine several extremal bounds for planar graphs to be supereulerian.
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