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A note on face coloring entire weightings of plane graphs

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Jendrol S., Šugerek P.

Discussiones Mathematicae Graph Theory

2014

tom 34

nr 2

421-426

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

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Jendrol S.

1 Šugerek P.

1 2014

Wyniki wyszukiwania

A note on face coloring entire weightings of plane graphs