Maximal k-independent sets in graphs

• Autorzy: Mostafa Blidia , Mustapha Chellali , Odile Favaron , Nacéra Meddah
• Języki publikacji: EN

Abstrakty

EN

A subset of vertices of a graph G is k-independent if it induces in G a subgraph of maximum degree less than k. The minimum and maximum cardinalities of a maximal k-independent set are respectively denoted iₖ(G) and βₖ(G). We give some relations between βₖ(G) and $β_j(G)$ and between iₖ(G) and $i_j(G)$ for j ≠ k. We study two families of extremal graphs for the inequality i₂(G) ≤ i(G) + β(G). Finally we give an upper bound on i₂(G) and a lower bound when G is a cactus.

Słowa kluczowe

EN

k-independent; cactus

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2008
• Tom: 28
• Numer: 1
• Strony: 151-163

Daty

wydano

2008

otrzymano

2007-01-18

poprawiono

2008-01-08

zaakceptowano

2008-01-08

Twórcy

autor

Mostafa Blidia

• LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270, Blida, Algeria

autor

Mustapha Chellali

• LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270, Blida, Algeria

autor

Odile Favaron

• Univ. Paris-Sud, LRI, URM 8623, Orsay, F-91405, France, CNRS, Orsay, F91405

autor

Nacéra Meddah

• LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270, Blida, Algeria

Bibliografia

• [1] M. Blidia, M. Chellali, O. Favaron and N. Meddah, On k-independence in graphs with emphasis on trees, Discrete Math. 307 (2007) 2209-2216, doi: 10.1016/j.disc.2006.11.007.
• [2] M. Borowiecki and D. Michalak, Generalized independence and domination in graphs, Discrete Math. 191 (1998) 51-56, doi: 10.1016/S0012-365X(98)00092-2.
• [3] O. Favaron, On a conjecture of Fink and Jacobson concerning k-domination and k-dependence, J. Combin. Theory (B) 39 (1985) 101-102, doi: 10.1016/0095-8956(85)90040-1.
• [4] O. Favaron, k-domination and k-independence in graphs, Ars Combin. 25 C (1988) 159-167.
• [5] J.F. Fink and M.S. Jacobson, n-domination, n-dependence and forbidden subgraphs, Graph Theory with Applications to Algorithms and Computer (John Wiley and sons, New York, 1985) 301-311.
• [6] G. Chartrand and L. Lesniak, Graphs & Digraphs: Third Edition (Chapman & Hall, London, 1996).
• [7] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).

Identyfikatory

DOI

10.7151/dmgt.1398