From Tripods to Bipods: Reducing the Queue Number of Planar Graphs Costs Just One Leg

As an alternative to previously existing planar graph product structure theorems, we prove that every planar graph G is a subgraph of the strong product of K_2, a path and a planar subgraph of a 4-tree. As an application, we show that the queue number of planar graphs is at most 38 whereas the queue number of planar bipartite graphs is at most 25.