Geodesic
Generalized circular colouring of graphs
Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 2, pp. 345-356

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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.
Keywords: graph property, P-colouring, circular colouring, strong circular P-chromatic number 
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Mihók, Peter; Oravcová, Janka; Soták, Roman. Generalized circular colouring of graphs. Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 2, pp. 345-356. http://geodesic.mathdoc.fr/item/DMGT_2011_31_2_a10/