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- W4238286799 abstract "Let $G$ be a planar graph drawn in the plane so that its outer boundary is a $k$-cycle. A four coloring of the outer boundary $gamma$ is admissible if there is a four coloring of $G$ which coincides with $gamma$ on the boundary. If $psi$ is the number of admissible boundary colorings, we show that the 4CC implies $psi geqslant 3 cdot {2^k}$ for $k = 3, cdots ,6$. We conjecture this to be true for all $k$ and show $psi$ is $geqslant c{((1 + {5^{1/2}})/2)^k}$. A graph is totally reducible (t.r.) if every boundary coloring is admissible. There are triangulations of the interior of a $k$-cycle which are t.r. for anv $k$. We investigate a class of graphs called annuli, characterize t.r. annuli and show that annuli satisfy the above conjecture." @default.
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- W4238286799 date "1973-07-01" @default.
- W4238286799 modified "2023-10-14" @default.
- W4238286799 title "Boundary Values in the Four Color Problem" @default.
- W4238286799 doi "https://doi.org/10.2307/1996646" @default.
- W4238286799 hasPublicationYear "1973" @default.
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