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A Note On Vertex Colorings Of Plane Graphs

100%

Fabricia I., Jendrol’ S., Soták R.

Discussiones Mathematicae Graph Theory

2014

tom 34

nr 4

849-855

Given an integer valued weighting of all elements of a 2-connected plane graph G with vertex set V , let c(v) denote the sum of the weight of v ∈ V and of the weights of all edges and all faces incident with v. This vertex coloring of G is proper provided that c(u) ≠ c(v) for any two adjacent vertices u and v of G. We show that for every 2-connected plane graph there is such a proper vertex coloring with weights in {1, 2, 3}. In a special case, the value 3 is improved to 2.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Fabricia I.

1 Jendrol’ S.

1 Soták R.

1 2014

Wyniki wyszukiwania

A Note On Vertex Colorings Of Plane Graphs