Tag Archives: four-colors theorem

Coloring Simple Polytopes and Triangulations

Coloring Edge-coloring of simple polytopes One of the equivalent formulation of the four-color theorem asserts that: Theorem (4CT) : Every cubic bridgeless planar graph is 3-edge colorable So we can color the edges by three colors such that every two … Continue reading

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Around Borsuk’s Conjecture 3: How to Save Borsuk’s conjecture

Borsuk asked in 1933 if every bounded set K of diameter 1 in can be covered by d+1 sets of smaller diameter. A positive answer was referred to as the “Borsuk Conjecture,” and it was disproved by Jeff Kahn and me in 1993. … Continue reading

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