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 |
| _version_ | 1797705880209195008 |
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| author | Štorgel Kenny |
| author_facet | Štorgel Kenny |
| author_sort | Štorgel Kenny |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T05:43:51Z |
| format | Article |
| id | doaj.art-c9489242c1b44470a6ff959f56bff2d5 |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T05:43:51Z |
| publishDate | 2023-02-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-c9489242c1b44470a6ff959f56bff2d52023-09-03T05:51:42ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922023-02-0143115115810.7151/dmgt.2357Improved Bounds for Some Facially Constrained ColoringsŠtorgel Kenny0Faculty of Information Studies, Novo mesto, Slovenia University of Primorska, FAMNIT, Koper, SloveniaA 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.https://doi.org/10.7151/dmgt.2357plane graphfacial coloringfacial-parity edge-coloringfacial-parity vertex-coloringworm coloring05c1505c10 |
| spellingShingle | Štorgel Kenny Improved Bounds for Some Facially Constrained Colorings Discussiones Mathematicae Graph Theory plane graph facial coloring facial-parity edge-coloring facial-parity vertex-coloring worm coloring 05c15 05c10 |
| title | Improved Bounds for Some Facially Constrained Colorings |
| title_full | Improved Bounds for Some Facially Constrained Colorings |
| title_fullStr | Improved Bounds for Some Facially Constrained Colorings |
| title_full_unstemmed | Improved Bounds for Some Facially Constrained Colorings |
| title_short | Improved Bounds for Some Facially Constrained Colorings |
| title_sort | improved bounds for some facially constrained colorings |
| topic | plane graph facial coloring facial-parity edge-coloring facial-parity vertex-coloring worm coloring 05c15 05c10 |
| url | https://doi.org/10.7151/dmgt.2357 |
| work_keys_str_mv | AT storgelkenny improvedboundsforsomefaciallyconstrainedcolorings |