A Note On Vertex Colorings Of Plane Graphs

• Autorzy: Igor Fabricia , Stanislav Jendrol’ , Roman Soták
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

plane graph; vertex coloring.

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 4
• Strony: 849-855

Daty

wydano

2014-11-01

otrzymano

2013-05-07

poprawiono

2014-01-13

zaakceptowano

2014-01-13

online

2014-11-15

Twórcy

autor

Igor Fabricia

• Institute of Mathematics P.J. ˇSafárik University Košice, Slovak Republic

autor

Stanislav Jendrol’

• Institut für Mathematik Technische Universität Ilmenau, Germany

autor

Roman Soták

• Institute of Mathematics P.J. ˇSafárik University Košice, Slovak Republic

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Identyfikatory

DOI

10.7151/dmgt.1771