We are given an euler planar graph $G$.
What is the number of colors required $G^{*}$ where $G^{*}$ denotes the dual of graph $G$? Please provide the answer in terms of the number of faces, vertices or edges in the graph.
I read here that "A planar bipartite graph is dual to a planar Eulerian graph and vice versa.". So is the answer to the above problem 2? If yes, how do we prove it.