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Generalized Fractional and Circular Total Colorings of Graphs

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Kemnitz A., Marangio M., Mihók P., Oravcová J., Soták R.

Discussiones Mathematicae Graph Theory

2015

tom 35

nr 3

517-532

Let P and Q be additive and hereditary graph properties, r, s ∈ N, r ≥ s, and [ℤr]s be the set of all s-element subsets of ℤr. An (r, s)-fractional (P,Q)-total coloring of G is an assignment h : V (G) ∪ E(G) → [ℤr]s such that for each i ∈ ℤr the following holds: the vertices of G whose color sets contain color i induce a subgraph of G with property P, edges with color sets containing color i induce a subgraph of G with property Q, and the color sets of incident vertices and edges are disjoint. If each vertex and edge of G is colored with a set of s consecutive elements of ℤr we obtain an (r, s)-circular (P,Q)-total coloring of G. In this paper we present basic results on (r, s)-fractional/circular (P,Q)-total colorings. We introduce the fractional and circular (P,Q)-total chromatic number of a graph and we determine this number for complete graphs and some classes of additive and hereditary properties.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Kemnitz A.

1 Marangio M.

1 Mihók P.

1 Oravcová J.

1 Soták R.

1 2015

Wyniki wyszukiwania

Generalized Fractional and Circular Total Colorings of Graphs