Fire-farve Sætningen

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Fire-farve Sætningen JB Oversigt Historie Kort og Grafer Bevis ide Kempekæder Beviserne Afladning Forbedringer og generaliseringer Andre overflader Ringel-Youngs sætningen - 1968 Heawood formel 7-farve sætningen Referencer Heawood formel - 1890 Lad G være indlejret p˚a en overflade med Euler-karakteristik ɛ. S˚a er (’=’ for ’pæne indlejringer). V − E + F ≥ ɛ Hver region har mindst 3 kanter: E ≥ 3F /2, dvs. V − ɛ ≥ E − F ≥ E/3, dvs. E ≤ 3V − 3ɛ
Fire-farve Sætningen JB Oversigt Historie Kort og Grafer Bevis ide Kempekæder Beviserne Afladning Forbedringer og generaliseringer Andre overflader Ringel-Youngs sætningen - 1968 Heawood formel 7-farve sætningen Referencer Heawood formel Lad G være minimal med χG = k. S˚a er δ(G) ≥ k − 1. Alts˚a er V (k − 1) ≤ deg(x) = 2E ≤ 6V − 6ɛ x∈V Alts˚a er for k ≥ 7: k(k − 7) ≤ V (k − 7) ≤ −6ɛ (idet V ≥ k). k(k − 7) + 6ɛ ≤ 0 k ≤ H(ɛ) = 7 + √ 49 − 24ɛ 2
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Fire-farve Sætningen

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