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. Gabriela Karafová, Roman Soták, Generalized Fractional Total Colorings of Graphs
  3. Arnfried Kemnitz, Peter Mihók, Margit Voigt, Fractional (P,Q)-Total List Colorings of Graphs
  4. Július Czap, Peter Mihók, Fractional Q-Edge-Coloring of Graphs
  5. Arnfried Kemnitz, Massimiliano Marangio, Peter Mihók, Janka Oravcová, Roman Soták, Generalized Fractional and Circular Total Colorings of Graphs

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