Every signed planar graph without cycles of length from 4 to 7 is 3-colorable
Abstract
Hu and Li investigate the signed graph version of Erdos problem: Is there a constant c such that every signed planar graph without k-cycles, where 4≤ k≤ c, is 3-colorable and prove that each signed planar graph without cycles of length from 4 to 8 is 3-colorable. We give a very short and simple proof of this result and improve it, based on a recent observation.
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