The biparticity of a graph
Frank Harary, Derbiau Hsu, Zevi Miller · Journal of Graph Theory · 1977
Abstract The biparticity β(G) of a graph G is the minimum number of bipartite graphs required to cover G. It is proved that for any graph G, β(G) = {log2χ(G)}. In view of the recent announcement of the Four Color Theorem, it follows that the biparticity of every planar graph is 2.