Fire-farve Sætningen

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Fire-farve Sætningen JB Oversigt Historie Kort og Grafer Bevis ide Kempekæder Beviserne Afladning Forbedringer og generaliseringer m-pires Jord-M˚ane problemet Liste-farvninger Andre overflader Referencer m-pires Hvert land har m regioner. Plan graf G = (V , E). Euler’s formel giver E ≤ 3(V − 2). Emperiegraf H = (v, e). V = mv, e ≤ E. x∈v deg H(x) = 2e ≤ 2E ≤ 6(V − 2) Gennemsnitsgraden er 2e v Induktion. ≤ 6(V − 2)/v = 6m(V − 2)/V < 6m Heawood fandt eksempel for m = 2 der kræver 12 farver. Heawood (1890): 2-pire løst. Jackson and Ringel (1984): m-pire løst.
Fire-farve Sætningen JB Oversigt Historie Kort og Grafer Bevis ide Kempekæder Beviserne Afladning Forbedringer og generaliseringer m-pires Jord-M˚ane problemet Liste-farvninger Andre overflader Referencer Kim Scott’s symmetriske 2-pire 10 1 4 3 1 11 11 6 5 6 5 4 7 8 9 8 10 9 7 12 12 2 2 3
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Fire-farve Sætningen

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