Relations between the domination parameters and the chromatic index of a graph
Discussiones Mathematicae Graph Theory (2009)
- Volume: 29, Issue: 3, page 615-627
- ISSN: 2083-5892
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topWłodzimierz Ulatowski. "Relations between the domination parameters and the chromatic index of a graph." Discussiones Mathematicae Graph Theory 29.3 (2009): 615-627. <http://eudml.org/doc/270801>.
@article{WłodzimierzUlatowski2009,
abstract = {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.},
author = {Włodzimierz Ulatowski},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {domination; domination parameters; chromatic index},
language = {eng},
number = {3},
pages = {615-627},
title = {Relations between the domination parameters and the chromatic index of a graph},
url = {http://eudml.org/doc/270801},
volume = {29},
year = {2009},
}
TY - JOUR
AU - Włodzimierz Ulatowski
TI - Relations between the domination parameters and the chromatic index of a graph
JO - Discussiones Mathematicae Graph Theory
PY - 2009
VL - 29
IS - 3
SP - 615
EP - 627
AB - 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.
LA - eng
KW - domination; domination parameters; chromatic index
UR - http://eudml.org/doc/270801
ER -
References
top- [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. Zbl0612.05056
- [4] T. Gallai, Über extreme Punkt-und Kantenmengen, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 2 (1959) 133-138. Zbl0094.36105
- [5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Decker Inc., New York, 1998). Zbl0890.05002
- [6] D. König, Graphok és alkalmazásuk a determinánsok és a halmazok elméletére, Math. Termész. Ért. 34 (1916) 104-119. Zbl46.1451.03
- [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).
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