We only consider finite graphs without loops or multiple edges. For a graph G, we useV (G) and E(G) to denote the vertex set and edge set of G, respectively. A k-walk in Gis a walk passing through every vertex of G at least once and at most k times. A circuitgraph (G, C) is a 2-connected plane graph G with outer cycle C such that for each 2-cutS in G, every component of G − S contains a vertex of C. It is immediate that every3-connected planar graph G is a circuit graph (we may choose C to be any facial cycle ofG).In 1994, Gao and Richter proved that every circuit graph contains a closed 2-walk. The existence of such a walk in every 3-connected planar graph was conjectured byJackson and Wormald . Gao, Richter, and Yu extended this result by showing thatevery 3-connected planar graph has a closed 2-walk such that any vertex visited twice isin a vertex...