Domination and independence subdivision numbers of graphs
Teresa W. Haynes, Sandra M. Hedetniemi, Stephen T. Hedetniemi (2000)
Discussiones Mathematicae Graph Theory
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The domination subdivision number of a graph is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the domination number. Arumugam showed that this number is at most three for any tree, and conjectured that the upper bound of three holds for any graph. Although we do not prove this interesting conjecture, we give an upper bound for the domination subdivision number for any graph G in terms of the minimum degrees of...