Let P and Q be additive and hereditary graph properties and let r, s be integers such that r ≥ s. Then an r/s -fractional (P,Q)-total coloring of a finite graph G = (V,E) is a mapping f, which assigns an s-element subset of the set {1, 2, . . . , r} to each vertex and each edge, moreover, for any color i all vertices of color i induce a subgraph with property P, all edges of color i induce a subgraph with property Q and vertices and incident edges have been assigned disjoint sets of colors. The minimum ratio of an r/s -fractional (P,Q)-total coloring of G is called fractional (P,Q)-total chromatic number χ″ƒ,P,Q(G) = r/ s . We show in this paper that χ″ƒ,P,Q of a graph G with o(V (G)) vertex orbits and o(E(G)) edge orbits can be found as a solution of a linear program with integer coefficients which consists only of o(V (G)) + o(E(G)) inequalities.
@article{bwmeta1.element.doi-10_7151_dmgt_1810,
author = {Gabriela Karafov\'a and Roman Sot\'ak},
title = {Generalized Fractional Total Colorings of Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {35},
year = {2015},
pages = {463-473},
zbl = {1317.05059},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1810}
}
Gabriela Karafová; Roman Soták. Generalized Fractional Total Colorings of Graphs. Discussiones Mathematicae Graph Theory, Tome 35 (2015) pp. 463-473. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1810/
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