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• # Artykuł - szczegóły

## Discussiones Mathematicae Graph Theory

2013 | 33 | 4 | 665-676

## Generalized Fractional Total Colorings of Complete Graph

EN

### Abstrakty

EN
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.

EN

665-676

wydano
2013-09-01
online
2013-10-15

### Twórcy

autor
• Institute of Mathematics, P.J. Šafárik University, Jesenná 5, 040 01 Košice, Slovakia

### Bibliografia

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