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    $\begingroup$ One basic source is: "The Four-color Problem: Assaults and Conquest" by Saaty and Kainen. It contains so many nice reformulations (over 120!). Could be useful to "parallel" a generalization. $\endgroup$ Commented Dec 9, 2014 at 22:56
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    $\begingroup$ mathoverflow.net/questions/273120/… is more about statements equivalent to the Four Color Theorem than about "generalizations, variations, and strengthenings," but still might be of some interest here. $\endgroup$ Commented May 19, 2021 at 6:05