Geodesic
Relations between the domination parameters and the chromatic index of a graph
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 615-627.

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

In this paper we show upper bounds for the sum and the product of the lower domination parameters and the chromatic index of a graph. We also present some families of graphs for which these upper bounds are achieved. Next, we give a lower bound for the sum of the upper domination parameters and the chromatic index. This lower bound is a function of the number of vertices of a graph and a new graph parameter which is defined here. In this case we also characterize graphs for which a respective equality holds.
Keywords: domination, domination parameters, chromatic index 
@article{DMGT_2009_29_3_a11,
     author = {Ulatowski, W{\l}odzimierz},
     title = {Relations between the domination parameters and the chromatic index of a graph},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {615--627},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a11/}
}
TY  - JOUR
AU  - Ulatowski, Włodzimierz
TI  - Relations between the domination parameters and the chromatic index of a graph
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2009
SP  - 615
EP  - 627
VL  - 29
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a11/
LA  - en
ID  - DMGT_2009_29_3_a11
ER  - 
%0 Journal Article
%A Ulatowski, Włodzimierz
%T Relations between the domination parameters and the chromatic index of a graph
%J Discussiones Mathematicae. Graph Theory
%D 2009
%P 615-627
%V 29
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a11/
%G en
%F DMGT_2009_29_3_a11
Ulatowski, Włodzimierz. Relations between the domination parameters and the chromatic index of a graph. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 615-627. http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a11/

[1] M. Chellalia and L. Volkmann, Relations between the lower domination parameters and the chromatic number of a graph, Discrete Math. 274 (2004) 1-8, doi: 10.1016/S0012-365X(03)00093-1.

[2] E.J. Cockayne, O. Favaron, C. Payan and A.G. Thomas, Contributions to the theory of domination, independence and irredundance in graphs, Discrete Math. 33 (1981) 249-258, doi: 10.1016/0012-365X(81)90268-5.

[3] O. Favaron, Stability, domination and irredundance in a graph, J. Graph Theory 10 (1986) 429-438, doi: 10.1002/jgt.3190100402.

[4] T. Gallai, Über extreme Punkt-und Kantenmengen, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 2 (1959) 133-138.

[5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Decker Inc., New York, 1998).

[6] D. König, Graphok és alkalmazásuk a determinánsok és a halmazok elméletére, Math. Termész. Ért. 34 (1916) 104-119.

[7] D. König, Graphs and matrices, Mat. Fiz. Lapok 38 (1931) 116-119 (in Hungarian).

[8] V.G. Vizing, On an estimate of the chromatic class of a p-graph, Metody Diskret. Analiz. 29 (1964) 25-30 (in Russian).