# Generalized circular colouring of graphs

• Volume: 31, Issue: 2, page 345-356
• ISSN: 2083-5892

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## Abstract

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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.

## How to cite

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Peter Mihók, Janka Oravcová, and Roman Soták. "Generalized circular colouring of graphs." Discussiones Mathematicae Graph Theory 31.2 (2011): 345-356. <http://eudml.org/doc/270811>.

@article{PeterMihók2011,
abstract = {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.},
author = {Peter Mihók, Janka Oravcová, Roman Soták},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {graph property; P-colouring; circular colouring; strong circular P-chromatic number; -colouring; strong circular -chromatic number},
language = {eng},
number = {2},
pages = {345-356},
title = {Generalized circular colouring of graphs},
url = {http://eudml.org/doc/270811},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Peter Mihók
AU - Janka Oravcová
AU - Roman Soták
TI - Generalized circular colouring of graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2011
VL - 31
IS - 2
SP - 345
EP - 356
AB - 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.
LA - eng
KW - graph property; P-colouring; circular colouring; strong circular P-chromatic number; -colouring; strong circular -chromatic number
UR - http://eudml.org/doc/270811
ER -

## References

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1. [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. Zbl0706.05022
2. [2] O. Borodin, On acyclic colouring of planar graphs, Discrete Math. 25 (1979) 211-236, doi: 10.1016/0012-365X(79)90077-3. Zbl0406.05031
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. [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. Zbl0902.05026
5. [5] W. Klostermeyer, Defective circular coloring, Austr. J. Combinatorics 26 (2002) 21-32. Zbl1009.05061
6. [6] P. Mihók, On the lattice of additive hereditary properties of object systems, Tatra Mt. Math. Publ. 30 (2005) 155-161. Zbl1150.05394
7. [7] P. Mihók, Zs. Tuza and M. Voigt, Fractional P-colourings and P-choice ratio, Tatra Mt. Math. Publ. 18 (1999) 69-77.
8. [8] A. Vince, Star chromatic number, J. Graph Theory 12 (1988) 551-559. Zbl0658.05028

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