Improved Bounds for Some Facially Constrained Colorings
A facial-parity edge-coloring of a 2-edge-connected plane graph is a facially-proper edge-coloring in which every face is incident with zero or an odd number of edges of each color. A facial-parity vertex-coloring of a 2-connected plane graph is a proper vertex-coloring in which every face is incide...
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2023-02-01
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| Series: | Discussiones Mathematicae Graph Theory |
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| Online Access: | https://doi.org/10.7151/dmgt.2357 |
| Summary: | A facial-parity edge-coloring of a 2-edge-connected plane graph is a facially-proper edge-coloring in which every face is incident with zero or an odd number of edges of each color. A facial-parity vertex-coloring of a 2-connected plane graph is a proper vertex-coloring in which every face is incident with zero or an odd number of vertices of each color. Czap and Jendroľ in [Facially-constrained colorings of plane graphs: A survey, Discrete Math. 340 (2017) 2691–2703], conjectured that 10 colors suffice in both colorings. We present an infinite family of counterexamples to both conjectures. |
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| ISSN: | 2083-5892 |