Abstract
AbstractFor a plane near‐triangulation with the outer face bounded by a cycle , let denote the function that to each 4‐coloring of assigns the number of ways extends to a 4‐coloring of . The Block‐count reducibility argument (which has been developed in connection with attempted proofs of the Four Color Theorem) is equivalent to the statement that the function belongs to a certain cone in the space of all functions from 4‐colorings of to real numbers. We investigate the properties of this cone for , formulate a conjecture strengthening the Four Color Theorem, and present evidence supporting this conjecture.
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