Abstract
We consider, for a plane graph G and a positive integer p, an edge coloring such that the set of colors used on each face of G contains at most p colors. The maximum number of colors for such a coloring is called the facial edge-p-visibility of G. We provide several general tight lower and upper bounds for this graph coloring invariant; moreover, for certain special families of plane graphs, we determine its exact values.
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Acknowledgements
This work was supported by the Slovak Research and Development Agency under the contract No. APVV-19-0153.
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Czap, J., Jendrol’, S. & Madaras, T. Facial Visibility in Edge Colored Plane Graphs. Graphs and Combinatorics 38, 4 (2022). https://doi.org/10.1007/s00373-021-02411-9
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DOI: https://doi.org/10.1007/s00373-021-02411-9