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The Heawood four-color graph is the 25-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof of the four-color theorem fails.
The Fritsch graph and Soifer graph provide smaller (and in fact the smallest possible) counterexamples.
Gethner, E. and Springer, W. M. II. "How False Is Kempe's Proof of the Four-Color Theorem?" Congr. Numer. 164, 159-175, 2003.
Kempe, A. B. "On the Geographical Problem of Four-Colors." Amer. J. Math. 2, 193-200, 1879.
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مخاطر عدم علاج ارتفاع ضغط الدم
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اختراق جديد في علاج سرطان البروستات العدواني
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مدرسة دار العلم.. صرح علميّ متميز في كربلاء لنشر علوم أهل البيت (عليهم السلام)
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