Generalized Fractional Total Colorings of Complete Graph
Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 4, p. 665.
Voir la notice de l'article dans European Digital Mathematics Library
An additive and hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let P and Q be two additive and hereditary graph properties and let r, s be integers such that r ≥ s Then an [...] 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 of property P, all edges of color i induce a subgraph of property Q and vertices and incident edges have assigned disjoint sets of colors. The minimum ratio [...] of an [...] - fractional (P,Q)-total coloring of G is called fractional (P,Q)-total chromatic number X″f,P,Q(G) = [...] Let k = sup{i : Ki+1 ∈ P} and l = sup{i Ki+1 ∈ Q}. We show for a complete graph Kn that if l ≥ k +2 then _X″f,P,Q(Kn) = [...] for a sufficiently large n.
@article{DMGT_2013__33_4_267837,
author = {Gabriela Karafov\'a},
title = {Generalized {Fractional} {Total} {Colorings} of {Complete} {Graph}},
journal = {Discussiones Mathematicae Graph Theory},
pages = {665},
publisher = {mathdoc},
volume = {33},
number = {4},
year = {2013},
zbl = {06323187},
language = {en},
url = {https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_4_267837/}
}
Gabriela Karafová. Generalized Fractional Total Colorings of Complete Graph. Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 4, p. 665. https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_4_267837/