Máčajová et al. (2016) defined the chromatic number of a signed graph which coincides for all-positive signed graphs with the chromatic number of unsigned graphs. They conjectured that in this setting, for signed planar graphs four colors are always enough, generalizing thereby The Four Color Theorem. We disprove the conjecture.

中文翻译：

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关于有符号图的四色定理

Máčajová等。（2016年）定义了一个有符号图的色数，它与所有正符号图的色数与无符号图的色数一致。他们推测，在这种情况下，对于有符号的平面图，四种颜色总是足够的，从而概括了四种颜色定理。我们反对这种猜想。