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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1540,
author = {Mieczys\l aw Borowiecki and Arnfried Kemnitz and Massimiliano Marangio and Peter Mih\'ok},
title = {Generalized total colorings of graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {31},
year = {2011},
pages = {209-222},
zbl = {1234.05076},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1540}
}
Mieczysław Borowiecki; Arnfried Kemnitz; Massimiliano Marangio; Peter Mihók. Generalized total colorings of graphs. Discussiones Mathematicae Graph Theory, Tome 31 (2011) pp. 209-222. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1540/
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