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Generalized Fractional Total Colorings of Complete Graph

100%

Karafová G.

Discussiones Mathematicae Graph Theory

2013

tom 33

nr 4

665-676

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.

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Generalized total colorings of graphs

88%

Borowiecki M., Kemnitz A., Marangio M., Mihók P.

Discussiones Mathematicae Graph Theory

2011

tom 31

nr 2

209-222

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.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Borowiecki M.

1 Karafová G.

1 Kemnitz A.

1 Marangio M.

1 Mihók P.

1 2013

1 2011

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Generalized Fractional Total Colorings of Complete Graph

Generalized total colorings of graphs