Geodesic
Generalized chromatic numbers and additive hereditary properties of graphs
Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 2, pp. 259-270.

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

An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. Let and be additive hereditary properties of graphs. The generalized chromatic number χ_() is defined as follows: χ_() = n iff ⊆ ⁿ but ⊊ ^n-1. We investigate the generalized chromatic numbers of the well-known properties of graphs ₖ, ₖ, ₖ, ₖ and ₖ.
Keywords: property of graphs, additive, hereditary, generalized chromatic number 
@article{DMGT_2002_22_2_a4,
     author = {Broere, Izak and Dorfling, Samantha and Jonck, Elizabeth},
     title = {Generalized chromatic numbers and additive hereditary properties of graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {259--270},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2002_22_2_a4/}
}
TY  - JOUR
AU  - Broere, Izak
AU  - Dorfling, Samantha
AU  - Jonck, Elizabeth
TI  - Generalized chromatic numbers and additive hereditary properties of graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2002
SP  - 259
EP  - 270
VL  - 22
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2002_22_2_a4/
LA  - en
ID  - DMGT_2002_22_2_a4
ER  - 
%0 Journal Article
%A Broere, Izak
%A Dorfling, Samantha
%A Jonck, Elizabeth
%T Generalized chromatic numbers and additive hereditary properties of graphs
%J Discussiones Mathematicae. Graph Theory
%D 2002
%P 259-270
%V 22
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2002_22_2_a4/
%G en
%F DMGT_2002_22_2_a4
Broere, Izak; Dorfling, Samantha; Jonck, Elizabeth. Generalized chromatic numbers and additive hereditary properties of graphs. Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 2, pp. 259-270. http://geodesic.mathdoc.fr/item/DMGT_2002_22_2_a4/

[1] 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.

[2] M. Borowiecki and P. Mihók, Hereditary properties of graphs, in: V.R. Kulli, ed., Advances in Graph Theory (Vishwa International Publication, Gulbarga, 1991) 41-68.

[3] I. Broere, M.J. Dorfling, J.E Dunbar and M. Frick, A path(ological) partition problem, Discuss. Math. Graph Theory 18 (1998) 113-125, doi: 10.7151/dmgt.1068.

[4] I. Broere, P. Hajnal and P. Mihók, Partition problems and kernels of graphs, Discuss. Math. Graph Theory 17 (1997) 311-313, doi: 10.7151/dmgt.1058.

[5] S.A. Burr and M.S. Jacobson, On inequalities involving vertex-partition parameters of graphs, Congr. Numer. 70 (1990) 159-170.

[6] G. Chartrand, D.P. Geller and S.T. Hedetniemi, A generalization of the chromatic number, Proc. Camb. Phil. Soc. 64 (1968) 265-271, doi: 10.1017/S0305004100042808.

[7] M. Frick and F. Bullock, Detour chromatic numbers, manuscript.

[8] P. Hajnal, Graph partitions (in Hungarian), Thesis, supervised by L. Lovász (J.A. University, Szeged, 1984).

[9] T.R. Jensen and B. Toft, Graph colouring problems (Wiley-Interscience Publications, New York, 1995).

[10] L. Lovász, On decomposition of graphs, Studia Sci. Math. Hungar 1 (1966) 237-238; MR34#1715.

[11] P. Mihók, Problem 4, p. 86 in: M. Borowiecki and Z. Skupień (eds), Graphs, Hypergraphs and Matroids (Zielona Góra, 1985).

[12] J. Nesetril and V. Rödl, Partitions of vertices, Comment. Math. Univ. Carolinae 17 (1976) 85-95; MR54#173.