A note on domination parameters in random graphs

• Autorzy: Anthony Bonato , Changping Wang
• Języki publikacji: EN

Abstrakty

EN

Domination parameters in random graphs G(n,p), where p is a fixed real number in (0,1), are investigated. We show that with probability tending to 1 as n → ∞, the total and independent domination numbers concentrate on the domination number of G(n,p).

Słowa kluczowe

EN

domination; random graphs; independent domination; total domination

Kategorie tematyczne

• 05C80: Random graphs
• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2008
• Tom: 28
• Numer: 2
• Strony: 335-343

Daty

wydano

2008

otrzymano

2008-01-11

poprawiono

2008-03-03

zaakceptowano

2008-03-03

Twórcy

autor

Anthony Bonato

• Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada, N2L 3C5

autor

Changping Wang

• Department of Mathematics, Ryerson University, Toronto, ON, Canada, M5B 2K3

Bibliografia

• [1] N. Alon and J. Spencer, The Probabilistic Method (Wiley, New York, 2000).
• [2] P.A. Dreyer, Applications and variations of domination in graphs, Ph.D. Dissertation, Department of Mathematics (Rutgers University, 2000).
• [3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).
• [4] T.W. Haynes, S.T. Hedetniemi and P.J. Slater (eds.), Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998).
• [5] S. Janson, T. Łuczak and A. Ruciński, Random Graphs (John Wiley and Sons, New York, 2000), doi: 10.1002/9781118032718.
• [6] C. Kaiser and K. Weber, Degrees and domination number of random graphs in the n-cube, Rostock. Math. Kolloq. 28 (1985) 18-32.
• [7] K. Weber, Domination number for almost every graph, Rostock. Math. Kolloq. 16 (1981) 31-43.
• [8] B. Wieland and A.P. Godbole, On the domination number of a random graph, The Electronic Journal of Combinatorics 8 (2001) #R37.
• [9] I.E. Zverovich and V.E. Zverovich, The domination parameters of cubic graphs, Graphs and Combinatorics 21 (2005) 277-288, doi: 10.1007/s00373-005-0608-1.

Identyfikatory

DOI

10.7151/dmgt.1409