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2015 | 35 | 3 | 517-532
Tytuł artykułu

Generalized Fractional and Circular Total Colorings of Graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let P and Q be additive and hereditary graph properties, r, s ∈ N, r ≥ s, and [ℤr]s be the set of all s-element subsets of ℤr. An (r, s)-fractional (P,Q)-total coloring of G is an assignment h : V (G) ∪ E(G) → [ℤr]s such that for each i ∈ ℤr the following holds: the vertices of G whose color sets contain color i induce a subgraph of G with property P, edges with color sets containing color i induce a subgraph of G with property Q, and the color sets of incident vertices and edges are disjoint. If each vertex and edge of G is colored with a set of s consecutive elements of ℤr we obtain an (r, s)-circular (P,Q)-total coloring of G. In this paper we present basic results on (r, s)-fractional/circular (P,Q)-total colorings. We introduce the fractional and circular (P,Q)-total chromatic number of a graph and we determine this number for complete graphs and some classes of additive and hereditary properties.
Wydawca
Rocznik
Tom
35
Numer
3
Strony
517-532
Opis fizyczny
Daty
wydano
2015-08-01
otrzymano
2014-05-08
poprawiono
2014-10-24
zaakceptowano
2014-10-24
online
2015-07-29
Twórcy
  • Computational Mathematics Technical University Braunschweig, Germany, a.kemnitz@tu-bs.de
autor
  • Mathematical Institute, Slovak Academy of Sciences Grešákova 6, 040 01 Košice, Slovak Republic
  • Department of Applied Mathematics and Business Informatics Faculty of Economics, Technical University B.Nĕmcovej 32, 040 01 Košice, Slovak Republic
  • Department of Applied Mathematics and Business Informatics Faculty of Economics, Technical University B.Nĕmcovej 32, 040 01 Košice, Slovak Republic, janka.oravcova@tuke.sk
autor
  • Institute of Mathematics Faculty of Science, P.J. Šafárik University Jesenná 5, 041 54 Košice, Slovak Republic, roman.sotak@upjs.sk
Bibliografia
  • [1] I. Bárány, A short proof of Kneser’s Conjecture, J. Combin. Theory Ser. A 25 (1978) 325-326. doi:10.1016/0097-3165(78)90023-7[Crossref]
  • [2] M. Borowiecki, A. Kemnitz, M. Marangio and P. Mihók, Generalized total colorings of graphs, Discuss. Math. Graph Theory 31 (2011) 209-222. doi:10.7151/dmgt.1540[WoS][Crossref]
  • [3] M. Borowiecki and P. Mihók, Hereditary properties of graphs, in: V.R. Kulli, Ed., Advances in Graph Theory, Vishwa International Publications, Gulbarga (1991) 42-69.
  • [4] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semaniˇsin, Survey of hereditary properties of graphs, Discuss. Math. Graph Theory 17 (1997) 5-50. doi:10.7151/dmgt.1037[Crossref]
  • [5] F.R.K. Chung, On the Ramsey numbers N(3, 3, . . . , 3; 2), Discrete Math. 5 (1973) 317-321. doi:10.1016/0012-365X(73)90125-8 [Crossref]
  • [6] M.J. Dorfling and S. Dorfling, Generalized edge-chromatic numbers and additive hereditary properties of graphs, Discuss. Math. Graph Theory 22 (2002) 349-359. doi:10.7151/dmgt.1180[Crossref]
  • [7] A. Hackmann and A. Kemnitz, Circular total colorings of graphs, Congr. Numer. 158 (2002) 43-50.
  • [8] R.P. Jones, Hereditary properties and P-chromatic numbers, in: Combinatorics, London Math. Soc. Lecture Note, (Cambridge Univ. Press, London) 13 (1974) 83-88.[Crossref]
  • [9] G. Karafová, Generalized fractional total coloring of complete graphs, Discuss. Math. Graph Theory 33 (2013) 665-676. doi:10.7151/dmgt.1697[Crossref]
  • [10] K. Kilakos and B. Reed, Fractionally colouring total graphs, Combinatorica 13 (1993) 435-440. doi:10.1007/BF01303515[Crossref]
  • [11] L. Lovász, Kneser’s conjecture, chromatic number, and homotopy, J. Combin. The- ory Ser. A 25 (1978) 319-324. doi:10.1016/0097-3165(78)90022-5[Crossref]
  • [12] P. Mihók, Zs. Tuza and M. Voigt, Fractional P-colourings and P-choice-ratio, Tatra Mt. Math. Publ. 18 (1999) 69-77.
  • [13] E.R. Scheinerman and D.H. Ullman, Fractional Graph Theory (John Wiley & Sons, New York, 1997). http://www.ams.jhu.edu/∼ers/fgt.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1812
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