05942345

j

05942345 Mih\'ok, Peter Oravcov\'a, Janka Sot\'ak, Roman Generalized circular colouring of graphs. Discuss. Math., Graph Theory 31, No. 2, 345-356 (2011). 2011 University of Zielona G\'ora Press, Zielona G\'ora EN graph property $\cal P$-colouring circular colouring strong circular $\cal P$-chromatic number

doi:10.7151/dmgt.1550

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