Every signed planar graph without cycles of length from 4 to 7 is 3-colorable

Lan Kaiyang; Liu Feng

Every signed planar graph without cycles of length from 4 to 7 is 3-colorable

Combinatorics 2022-05-04 v2

Authors: Lan Kaiyang , Liu Feng

Abstract

Hu and Li investigate the signed graph version of Erd $\ddot{\mathrm{o}}$ s problem: Is there a constant $c$ such that every signed planar graph without $k$ -cycles, where $4\leq k\leq c$ , 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.

Keywords

signed planar graph cycle length 3-colorable erdos problem graph coloring

Cite

@article{arxiv.2205.00887,
  title  = {Every signed planar graph without cycles of length from 4 to 7 is 3-colorable},
  author = {Lan Kaiyang and Liu Feng},
  journal= {arXiv preprint arXiv:2205.00887},
  year   = {2022}
}

Comments

incomplete proof

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