# A note on face coloring entire weightings of plane graphs

Stanislav Jendrol; Peter Šugerek

Discussiones Mathematicae Graph Theory (2014)

- Volume: 34, Issue: 2, page 421-426
- ISSN: 2083-5892

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topStanislav Jendrol, and Peter Šugerek. "A note on face coloring entire weightings of plane graphs." Discussiones Mathematicae Graph Theory 34.2 (2014): 421-426. <http://eudml.org/doc/267708>.

@article{StanislavJendrol2014,

abstract = {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},

author = {Stanislav Jendrol, Peter Šugerek},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {entire weighting; plane graph; face colouring},

language = {eng},

number = {2},

pages = {421-426},

title = {A note on face coloring entire weightings of plane graphs},

url = {http://eudml.org/doc/267708},

volume = {34},

year = {2014},

}

TY - JOUR

AU - Stanislav Jendrol

AU - Peter Šugerek

TI - A note on face coloring entire weightings of plane graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2014

VL - 34

IS - 2

SP - 421

EP - 426

AB - 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

LA - eng

KW - entire weighting; plane graph; face colouring

UR - http://eudml.org/doc/267708

ER -

## References

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