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Community Bot
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Already for $d=3$ the boundary complex of the cyclic polytope with n vertices has a complete graph and hence requires $n$ colors.

You may ask if restricting the class of triangulations can lead to interesting extension of the FCT. Some answers in Generalizations of the four-color theoremGeneralizations of the four-color theorem are relevant.

Already for $d=3$ the boundary complex of the cyclic polytope with n vertices has a complete graph and hence requires $n$ colors.

You may ask if restricting the class of triangulations can lead to interesting extension of the FCT. Some answers in Generalizations of the four-color theorem are relevant.

Already for $d=3$ the boundary complex of the cyclic polytope with n vertices has a complete graph and hence requires $n$ colors.

You may ask if restricting the class of triangulations can lead to interesting extension of the FCT. Some answers in Generalizations of the four-color theorem are relevant.

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Gil Kalai
Gil Kalai
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Already for $d=3$ the boundary complex of the cyclic polytope with n vertices has a complete graph and hence requires $n$ colors.

You may ask if restricting the class of triangulations can lead to interesting extension of the FCT. Some answers in Generalizations of the four-color theorem are relevant.