A Note On Vertex Colorings Of Plane Graphs

Igor Fabricia; Stanislav Jendrol’; Roman Soták

Discussiones Mathematicae Graph Theory (2014)

  • Volume: 34, Issue: 4, page 849-855
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Igor Fabricia, Stanislav Jendrol’, and Roman Soták. "A Note On Vertex Colorings Of Plane Graphs." Discussiones Mathematicae Graph Theory 34.4 (2014): 849-855. <http://eudml.org/doc/269816>.

@article{IgorFabricia2014,
abstract = {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.},
author = {Igor Fabricia, Stanislav Jendrol’, Roman Soták},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {plane graph; vertex coloring.; vertex coloring},
language = {eng},
number = {4},
pages = {849-855},
title = {A Note On Vertex Colorings Of Plane Graphs},
url = {http://eudml.org/doc/269816},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Igor Fabricia
AU - Stanislav Jendrol’
AU - Roman Soták
TI - A Note On Vertex Colorings Of Plane Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2014
VL - 34
IS - 4
SP - 849
EP - 855
AB - 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.
LA - eng
KW - plane graph; vertex coloring.; vertex coloring
UR - http://eudml.org/doc/269816
ER -

References

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