By Ainouche A., Schiermeyer I.
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Additional resources for 0-Dual Closures for Several Classes of Graphs
Figure 15: A cubic map with twelve pentagons A reducible configuration is any configuration of regions that cannot occur in a minimum counterexample of the Four Color Conjecture. Many mathematicians who attempted to solve the Four Color Problem attempted to do so by trying to find an unavoidable set S of reducible configurations. Since S is unavoidable, this means that every cubic map must contain at least one configuration in S.
0-Dual Closures for Several Classes of Graphs by Ainouche A., Schiermeyer I.