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Generalized circular colouring of graphs

100%

Mihók P., Oravcová J., Soták R.

Discussiones Mathematicae Graph Theory

2011

tom 31

nr 2

345-356

Let P be a graph property and r,s ∈ N, r ≥ s. A strong circular (P,r,s)-colouring of a graph G is an assignment f:V(G) → {0,1,...,r-1}, such that the edges uv ∈ E(G) satisfying |f(u)-f(v)| < s or |f(u)-f(v)| > r - s, induce a subgraph of G with the propery P. In this paper we present some basic results on strong circular (P,r,s)-colourings. We introduce the strong circular P-chromatic number of a graph and we determine the strong circular P-chromatic number of complete graphs for additive and hereditary graph properties.

Generalized Fractional and Circular Total Colorings of Graphs

88%

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

2 Discussiones Mathematicae Graph Theory

2 Mihók P.

2 Oravcová J.

2 Soták R.

1 Kemnitz A.

1 Marangio M.

1 2015

1 2011

Wyniki wyszukiwania

Generalized circular colouring of graphs

Generalized Fractional and Circular Total Colorings of Graphs