Generalized total colorings of graphs

Mieczysław Borowiecki; Arnfried Kemnitz; Massimiliano Marangio; Peter Mihók

Discussiones Mathematicae Graph Theory (2011)

  • Volume: 31, Issue: 2, page 209-222
  • ISSN: 2083-5892

Abstract

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An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let P and Q be additive hereditary properties of graphs. A (P,Q)-total coloring of a simple graph G is a coloring of the vertices V(G) and edges E(G) of G such that for each color i the vertices colored by i induce a subgraph of property P, the edges colored by i induce a subgraph of property Q and incident vertices and edges obtain different colors. In this paper we present some general basic results on (P,Q)-total colorings. We determine the (P,Q)-total chromatic number of paths and cycles and, for specific properties, of complete graphs. Moreover, we prove a compactness theorem for (P,Q)-total colorings.

How to cite

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Mieczysław Borowiecki, et al. "Generalized total colorings of graphs." Discussiones Mathematicae Graph Theory 31.2 (2011): 209-222. <http://eudml.org/doc/270805>.

@article{MieczysławBorowiecki2011,
abstract = {An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let P and Q be additive hereditary properties of graphs. A (P,Q)-total coloring of a simple graph G is a coloring of the vertices V(G) and edges E(G) of G such that for each color i the vertices colored by i induce a subgraph of property P, the edges colored by i induce a subgraph of property Q and incident vertices and edges obtain different colors. In this paper we present some general basic results on (P,Q)-total colorings. We determine the (P,Q)-total chromatic number of paths and cycles and, for specific properties, of complete graphs. Moreover, we prove a compactness theorem for (P,Q)-total colorings.},
author = {Mieczysław Borowiecki, Arnfried Kemnitz, Massimiliano Marangio, Peter Mihók},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {hereditary properties; generalized total colorings; paths; cycles; complete graphs},
language = {eng},
number = {2},
pages = {209-222},
title = {Generalized total colorings of graphs},
url = {http://eudml.org/doc/270805},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Mieczysław Borowiecki
AU - Arnfried Kemnitz
AU - Massimiliano Marangio
AU - Peter Mihók
TI - Generalized total colorings of graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2011
VL - 31
IS - 2
SP - 209
EP - 222
AB - An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let P and Q be additive hereditary properties of graphs. A (P,Q)-total coloring of a simple graph G is a coloring of the vertices V(G) and edges E(G) of G such that for each color i the vertices colored by i induce a subgraph of property P, the edges colored by i induce a subgraph of property Q and incident vertices and edges obtain different colors. In this paper we present some general basic results on (P,Q)-total colorings. We determine the (P,Q)-total chromatic number of paths and cycles and, for specific properties, of complete graphs. Moreover, we prove a compactness theorem for (P,Q)-total colorings.
LA - eng
KW - hereditary properties; generalized total colorings; paths; cycles; complete graphs
UR - http://eudml.org/doc/270805
ER -

References

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  10. [10] A. Kemnitz and M. Marangio, [r,s,t] -colorings of graphs, Discrete Math. 307 (2007) 199-207, doi: 10.1016/j.disc.2006.06.030. 
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  12. [12] P. Mihók and G. Semanišin, Unique factorization theorem and formal concept analysis, in: S. Ben Yahia et al. (eds.): Concept Lattices and Their Applications. Fourth International Conference, CLA 2006, Tunis, Tunisia, October 30-November 1, 2006. LNAI 4923. (Springer, Berlin, 2008) pp. 231-238. Zbl1133.05306
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Citations in EuDML Documents

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  1. Gabriela Karafová, Generalized Fractional Total Colorings of Complete Graph
  2. Mieczysław Borowiecki, Izak Broere, Hamiltonicity and Generalised Total Colourings of Planar Graphs
  3. Gabriela Karafová, Roman Soták, Generalized Fractional Total Colorings of Graphs
  4. Arnfried Kemnitz, Peter Mihók, Margit Voigt, Fractional (P,Q)-Total List Colorings of Graphs
  5. Július Czap, Peter Mihók, Fractional Q-Edge-Coloring of Graphs
  6. Arnfried Kemnitz, Massimiliano Marangio, Peter Mihók, Janka Oravcová, Roman Soták, Generalized Fractional and Circular Total Colorings of Graphs

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