We prove a two-point concentration for the independent domination number of the random graph provided p²ln(n) ≥ 64ln((lnn)/p).
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1533, author = {Lane Clark and Darin Johnson}, title = {The independent domination number of a random graph}, journal = {Discussiones Mathematicae Graph Theory}, volume = {31}, year = {2011}, pages = {129-142}, zbl = {1284.05244}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1533} }
Lane Clark; Darin Johnson. The independent domination number of a random graph. Discussiones Mathematicae Graph Theory, Tome 31 (2011) pp. 129-142. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1533/
[000] [1] N. Alon and J. Spencer, The Probabilistic Method (John Wiley, New York, 1992). | Zbl 0767.05001
[001] [2] B. Bollobás, Random Graphs (Second Edition, Cambridge University Press, New York, 2001).
[002] [3] A. Bonato and C. Wang, A note on domination parameters in random graphs, Discuss. Math. Graph Theory 28 (2008) 307-322, doi: 10.7151/dmgt.1409. | Zbl 1156.05040
[003] [4] A. Godbole and B. Wieland, On the domination number of a Random graph, Electronic J. Combin. 8 (2001) 1-13. | Zbl 0989.05108
[004] [5] T. Haynes, S. Hedetniemi and P. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, Inc., New York, 1998). | Zbl 0890.05002
[005] [6] T. Haynes, S. Hedetniemi and P. Slater, Domination in Graphs: Advanced Topics (Marcel Dekker, Inc., New York, 1998). | Zbl 0883.00011
[006] [7] K. Weber, Domination number for almost every graph, Rostocker Matematisches Kolloquium 16 (1981) 31-43. | Zbl 0476.05067