# Decompositions of Plane Graphs Under Parity Constrains Given by Faces

Discussiones Mathematicae Graph Theory (2013)

- Volume: 33, Issue: 3, page 521-530
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topJúlius Czap, and Zsolt Tuza. "Decompositions of Plane Graphs Under Parity Constrains Given by Faces." Discussiones Mathematicae Graph Theory 33.3 (2013): 521-530. <http://eudml.org/doc/268185>.

@article{JúliusCzap2013,

abstract = {An edge coloring of a plane graph G is facially proper if no two faceadjacent edges of G receive the same color. A facial (facially proper) parity edge coloring of a plane graph G is an (facially proper) edge coloring with the property that, for each color c and each face f of G, either an odd number of edges incident with f is colored with c, or color c does not occur on the edges of f. In this paper we deal with the following question: For which integers k does there exist a facial (facially proper) parity edge coloring of a plane graph G with exactly k colors?},

author = {Július Czap, Zsolt Tuza},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {plane graph; parity partition; edge coloring; facial parity edge coloringfacial; facially proper parity edge coloring},

language = {eng},

number = {3},

pages = {521-530},

title = {Decompositions of Plane Graphs Under Parity Constrains Given by Faces},

url = {http://eudml.org/doc/268185},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Július Czap

AU - Zsolt Tuza

TI - Decompositions of Plane Graphs Under Parity Constrains Given by Faces

JO - Discussiones Mathematicae Graph Theory

PY - 2013

VL - 33

IS - 3

SP - 521

EP - 530

AB - An edge coloring of a plane graph G is facially proper if no two faceadjacent edges of G receive the same color. A facial (facially proper) parity edge coloring of a plane graph G is an (facially proper) edge coloring with the property that, for each color c and each face f of G, either an odd number of edges incident with f is colored with c, or color c does not occur on the edges of f. In this paper we deal with the following question: For which integers k does there exist a facial (facially proper) parity edge coloring of a plane graph G with exactly k colors?

LA - eng

KW - plane graph; parity partition; edge coloring; facial parity edge coloringfacial; facially proper parity edge coloring

UR - http://eudml.org/doc/268185

ER -

## References

top- [1] J. Czap, S. Jendroľ, F. Kardoš and R. Sotak, Facial parity edge coloring of plane pseudographs, Discrete Math. 312 (2012) 2735-2740. doi:10.1016/j.disc.2012.03.036[Crossref][WoS] Zbl1245.05044
- [2] J. Czap and Zs. Tuza, Partitions of graphs and set systems under parity constraints, preprint (2011).
- [3] D. Gon，calves, Edge partition of planar graphs into two outerplanar graphs, Proceedings of the 37th Annual ACM Symposium on Theory of Computing (2005) 504-512. doi:10.1145/1060590.1060666[Crossref]
- [4] S. Grunewald, Chromatic index critical graphs and multigraphs, PhD Thesis, Universitat Bielefeld (2000). Zbl0947.05030
- [5] A. Kotzig, Contribution to the theory of Eulerian polyhedra, Mat.-Fyz. Cas. SAV (Math. Slovaca) 5 (1955) 101-113 (in Slovak).
- [6] T. Matrai, Covering the edges of a graph by three odd subgraphs, J. Graph Theory 53 (2006) 75-82. doi:10.1002/jgt.20170[Crossref] Zbl1098.05067
- [7] C.St.J.A. Nash-Williams, Decomposition of finite graphs into forests, J. London Math. Soc. 39 (1964) 12-12. doi:10.1112/jlms/s1-39.1.12[Crossref] Zbl0119.38805
- [8] L. Pyber, Covering the edges of a graph by . . . , Colloquia Mathematica Societatis Janos Bolyai, 60. Sets, Graphs and Numbers (1991) 583-610. Zbl0792.05110
- [9] D.P. Sanders and Y. Zhao, Planar graphs of maximum degree seven are class I, J. Combin. Theory (B) 83 (2001) 201-212. doi:10.1006/jctb.2001.2047[Crossref] Zbl1024.05031
- [10] V.G. Vizing, On an estimate of the chromatic class of a p-graph, Diskret. Analiz 3 (1964) 25-30.
- [11] L. Zhang, Every planar graph with maximum degree 7 is class I, Graphs Combin. 16 (2000) 467-495. doi:10.1007/s003730070009 [Crossref] Zbl0988.05042

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.