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

Voir la notice de l'article provenant de la source Library of Science

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 
@article{DMGT_2011_31_2_a10,
     author = {Mih\'ok, Peter and Oravcov\'a, Janka and Sot\'ak, Roman},
     title = {Generalized circular colouring of graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {345--356},
     publisher = {mathdoc},
     volume = {31},
     number = {2},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2011_31_2_a10/}
}
TY  - JOUR
AU  - Mihók, Peter
AU  - Oravcová, Janka
AU  - Soták, Roman
TI  - Generalized circular colouring of graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2011
SP  - 345
EP  - 356
VL  - 31
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2011_31_2_a10/
LA  - en
ID  - DMGT_2011_31_2_a10
ER  - 
%0 Journal Article
%A Mihók, Peter
%A Oravcová, Janka
%A Soták, Roman
%T Generalized circular colouring of graphs
%J Discussiones Mathematicae. Graph Theory
%D 2011
%P 345-356
%V 31
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2011_31_2_a10/
%G en
%F DMGT_2011_31_2_a10
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/

[1] J.A. Bondy and P. Hell, A Note on the Star Chromatic Number, J. Graph Theory 14 (1990) 479-482, doi: 10.1002/jgt.3190140412.

[2] O. Borodin, On acyclic colouring of planar graphs, Discrete Math. 25 (1979) 211-236, doi: 10.1016/0012-365X(79)90077-3.

[3] M. Borowiecki and P. Mihók, Hereditary properties of graphs, in: V.R. Kulli, editor, Advances in Graph Theory (Vishwa International Publishers, 1991) 42-69.

[4] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, A survey of hereditary properties of graphs, Discuss. Math. Graph Theory 17 (1997) 5-50, doi: 10.7151/dmgt.1037.

[5] W. Klostermeyer, Defective circular coloring, Austr. J. Combinatorics 26 (2002) 21-32.

[6] P. Mihók, On the lattice of additive hereditary properties of object systems, Tatra Mt. Math. Publ. 30 (2005) 155-161.

[7] P. Mihók, Zs. Tuza and M. Voigt, Fractional P-colourings and P-choice ratio, Tatra Mt. Math. Publ. 18 (1999) 69-77.

[8] A. Vince, Star chromatic number, J. Graph Theory 12 (1988) 551-559.