A counterexample to a conjecture on facial unique-maximal colorings

@article{Lidick2018ACT,
  title={A counterexample to a conjecture on facial unique-maximal colorings},
  author={Bernard Lidick{\'y} and Kacy Messerschmidt and Riste Skrekovski},
  journal={Discret. Appl. Math.},
  year={2018},
  volume={237},
  pages={123-125}
}
  • Bernard Lidický, Kacy Messerschmidt, Riste Skrekovski
  • Published 2018
  • Mathematics, Computer Science
  • Discret. Appl. Math.
  • Abstract A facial unique-maximum coloring of a plane graph is a proper vertex coloring by natural numbers where on each face α the maximal color appears exactly once on the vertices of α . Fabrici and Goring (2016) proved that six colors are enough for any plane graph and conjectured that four colors suffice. This conjecture is a strengthening of the Four Color Theorem. Wendland (2016) later decreased the upper bound from six to five. In this note, we disprove the conjecture by giving an… CONTINUE READING

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    Facial unique-maximum colorings of plane graphs with restriction on big vertices

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    Facial Colorings of Plane Graphs

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