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  • \$\begingroup\$ Nice effort, but I do believe you are missing one component. What about the case where a node is surrounded by 5 different colors? \$\endgroup\$ Commented Aug 15, 2018 at 17:50
  • \$\begingroup\$ I'll try to build a test case to break this \$\endgroup\$ Commented Aug 15, 2018 at 17:51
  • \$\begingroup\$ Suppose that a given node in your graph is surrounded by 5 other nodes, which you've already colored the 5 colors you are allowed. \$\endgroup\$ Commented Aug 15, 2018 at 17:56
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    \$\begingroup\$ My code randomly generates graph colorings and checks them until it generates a correct graph coloring, which it then prints upon exiting. In the case you describe it'd start over and hopefully not color those 5 nodes all 5 available colors. \$\endgroup\$ Commented Aug 15, 2018 at 17:59
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    \$\begingroup\$ Now it checks all the colorings in lexicographic order :) so it's deterministic and O(5^n), but a lot slower for most inputs. \$\endgroup\$ Commented Aug 15, 2018 at 18:09