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2013 | 33 | 3 | 521-530
Tytuł artykułu

Decompositions of Plane Graphs Under Parity Constrains Given by Faces

Treść / Zawartość
Warianty tytułu
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
Wydawca
Rocznik
Tom
33
Numer
3
Strony
521-530
Opis fizyczny
Daty
wydano
2013-07-01
online
2013-07-30
Twórcy
autor
  • Department of Applied Mathematics and Business Informatics, Faculty of Economics, Technical University of Košice, Němcovej 32, SK-040 01 Košice, Slovakia, julius.czap@tuke.sk
autor
  • 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, tuza@dcs.uni-pannon.hu
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]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1690
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