Geodesic
A note on face coloring entire weightings of plane graphs
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 2, pp. 421-426

Voir la notice de l'article provenant de la source Library of Science

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 α and also the weight of α. Such an entire weighting is a proper face colouring provided that f(α) ≠ f(β) for every two faces α and β 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.
Keywords: entire weighting, plane graph, face colouring 
@article{DMGT_2014_34_2_a15,
     author = {Jendrol, Stanislav and \v{S}ugerek, Peter},
     title = {A note on face coloring entire weightings of plane graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {421--426},
     publisher = {mathdoc},
     volume = {34},
     number = {2},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2014_34_2_a15/}
}
TY  - JOUR
AU  - Jendrol, Stanislav
AU  - Šugerek, Peter
TI  - A note on face coloring entire weightings of plane graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2014
SP  - 421
EP  - 426
VL  - 34
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2014_34_2_a15/
LA  - en
ID  - DMGT_2014_34_2_a15
ER  - 
%0 Journal Article
%A Jendrol, Stanislav
%A Šugerek, Peter
%T A note on face coloring entire weightings of plane graphs
%J Discussiones Mathematicae. Graph Theory
%D 2014
%P 421-426
%V 34
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2014_34_2_a15/
%G en
%F DMGT_2014_34_2_a15
Jendrol, Stanislav; Šugerek, Peter. A note on face coloring entire weightings of plane graphs. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 2, pp. 421-426. http://geodesic.mathdoc.fr/item/DMGT_2014_34_2_a15/