Four color theorem: counterexample to the hypothesis I was verifying :-(


Bad news … to me!

This example it is a counterexample to the hypothesis I was trying to verify!

Map signature: 1b+, 4b+, 6b+, 15b+, 7b-, 14b-, 8b-, 12b-, 13b-, 11b-, 9b-, 8e-, 7e-, 5b-, 6e-, 9e-, 10b-, 5e-, 4e-, 3b-, 10e-, 11e-, 12e-, 3e-, 2b-, 13e-, 14e-, 15e+, 2e+, 1e+

😦

For this example, no Kempe color switching exists along the main chain (b-r) = (1-2-3-4-5-6-7-8) that “divert” it, to make it end at a different vertex than vx. All other chains (*-g) along the main chain (b-r) involve vx or vy.

hypothesis-counterexample-v2

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One Response to Four color theorem: counterexample to the hypothesis I was verifying :-(

  1. Pingback: Four color theorem: experimenting impasses (as in life) | Four color theorem

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