A note on face coloring entire weightings of plane graphs
Given a weighting of all elements of a 2-connected plane graph G = (V,E, F), let f(α) denote the sum of the weights of the edges and vertices incident with the face _ and also the weight of _. Such an entire weighting is a proper face colouring provided that f(α) ≠ f(β) for every two faces α and _ s...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2014-05-01
|
| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.1738 |
| Summary: | Given a weighting of all elements of a 2-connected plane graph G = (V,E, F), let f(α) denote the sum of the weights of the edges and vertices incident with the face _ and also the weight of _. Such an entire weighting is a proper face colouring provided that f(α) ≠ f(β) for every two faces α and _ sharing an edge. We show that for every 2-connected plane graph there is a proper face-colouring entire weighting with weights 1 through 4. For some families we improved 4 to 3 |
|---|---|
| ISSN: | 2083-5892 |