# 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

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topMieczysław 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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## Citations in EuDML Documents

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