Decompositions of Plane Graphs Under Parity Constrains Given by Faces

• Autorzy: Július Czap , Zsolt Tuza
• Języki publikacji: EN

Abstrakty

EN

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?

Słowa kluczowe

EN

plane graph; parity partition; edge coloring

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2013
• Tom: 33
• Numer: 3
• Strony: 521-530

Daty

wydano

2013-07-01

online

2013-07-30

Twórcy

autor

Július Czap

• Department of Applied Mathematics and Business Informatics, Faculty of Economics, Technical University of Košice, Němcovej 32, SK-040 01 Košice, Slovakia

autor

Zsolt Tuza

• Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, H-1053 Budapest, Reáltanoda u. 13–15, Hungary and Department of Computer Science and Systems Technology University of Pannonia, H-8200 Veszprém, Egyetem u. 10, Hungary

Bibliografia

• [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]
• [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).
• [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]
• [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]
• [8] L. Pyber, Covering the edges of a graph by . . . , Colloquia Mathematica Societatis Janos Bolyai, 60. Sets, Graphs and Numbers (1991) 583-610.
• [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]
• [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]

Identyfikatory

DOI

10.7151/dmgt.1690