PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1998 | 18 | 1 | 127-142
Tytuł artykułu

An inequality chain of domination parameters for trees

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove that the smallest cardinality of a maximal packing in any tree is at most the cardinality of an R-annihilated set. As a corollary to this result we point out that a set of parameters of trees involving packing, perfect neighbourhood, R-annihilated, irredundant and dominating sets is totally ordered. The class of trees for which all these parameters are equal is described and we give an example of a tree in which most of them are distinct.
Wydawca
Rocznik
Tom
18
Numer
1
Strony
127-142
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-10-30
Twórcy
  • Department of Mathematics, University of Victoria, Victoria, British Columbia, Canada V8W 3P4
autor
  • LRI, Bât. 490, Université de Paris-Sud, Orsay, France 91405
autor
  • LRI, Bât. 490, Université de Paris-Sud, Orsay, France 91405
  • Department of Mathematics, University of South Africa, PO Box 392, 0003 Pretoria, South Africa
Bibliografia
  • [1] E.J. Cockayne, O. Favaron, C.M. Mynhardt and J. Puech, A characterisation of (γ,i)-trees, (preprint).
  • [2] E.J. Cockayne, O. Favaron, C.M. Mynhardt and J. Puech, Packing, perfect neighbourhood, irredundant and R-annihilated sets in graphs, Austr. J. Combin. Math. (to appear).
  • [3] E.J. Cockayne, P.J. Grobler, S.T. Hedetniemi and A.A. McRae, What makes an irredundant set maximal?, J. Combin. Math. Combin. Comput. (to appear).
  • [4] E.J. Cockayne, J.H. Hattingh, S.M. Hedetniemi, S.T. Hedetniemi and A.A. McRae, Using maximality and minimality conditions to construct inequality chains, Discrete Math. 176 (1997) 43-61, doi: 10.1016/S0012-365X(96)00356-1.
  • [5] E.J. Cockayne, S.M. Hedetniemi, S.T. Hedetniemi and C.M. Mynhardt, Irredundant and perfect neighbourhood sets in trees, Discrete Math. (to appear).
  • [6] E.J. Cockayne and C.M. Mynhardt, On a conjecture concerning irredundant and perfect neighbourhood sets in graphs, J. Combin. Math. Combin. Comput. (to appear).
  • [7] O. Favaron and J. Puech, Irredundant and perfect neighbourhood sets in graphs and claw-free graphs, Discrete Math. (to appear).
  • [8] G.H. Fricke, T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi and M.A. Henning, Perfect neighborhoods in graphs, (preprint).
  • [9] B.L. Hartnell, On maximal radius two independent sets, Congr. Numer. 48 (1985) 179-182.
  • [10] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs (Marcel Dekker, 1997).
  • [11] A. Meir and J.W. Moon, Relations between packing and covering numbers of a tree, Pacific J. Math. 61 (1975) 225-233.
  • [12] J. Puech, Irredundant and independent perfect neighborhood sets in graphs, (preprint).
  • [13] J. Topp and L. Volkmann, On packing and covering numbers of graphs, Discrete Math. 96 (1991) 229-238, doi: 10.1016/0012-365X(91)90316-T.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1069
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.