= Tait graph
{c}
= Checkerboard graph of a link diagram
{synonym}
Choose a checkerboard coloring of the complementary regions of a <link diagram>. The Tait graph has one vertex for each black region and one edge through each crossing joining its adjacent black regions. The other coloring gives its planar dual. For a connected <alternating link diagram>, all-A and all-B smoothing <circles> correspond to the regions of its two checkerboard colors; one-circle smoothing states correspond to <spanning trees>.
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