Subgraphs of 4-Regular Planar Graphs

We shall present an algorithm for determining whether or not a given planar graph H can ever be a subgraph of a 4-regular planar graph. The algorithm has running time O (| H | 2.5 ) and can be used to find an explicit 4-regular planar graph G ⊃ H if such a graph exists. It shall not matter whether we specify that H and G must be simple graphs or allow them to be multigraphs.