Relations between the domination parameters and the chromatic index of a graph

• Autorzy: Włodzimierz Ulatowski
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

domination; domination parameters; chromatic index

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2009
• Tom: 29
• Numer: 3
• Strony: 615-627

Daty

wydano

2009

otrzymano

2008-09-19

poprawiono

2008-10-23

zaakceptowano

2008-11-13

Twórcy

autor

Włodzimierz Ulatowski

• Faculty of Physics and Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-952 Gdańsk, Poland

Bibliografia

• [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).

Identyfikatory

DOI

10.7151/dmgt.1468