Bondage number of planar graphs without small cycles - Hou, Jianteng; Liu, Guizhen; Wu, Jianliang (Utilitas Mathematica, 2011)
The bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater than γ(G), where γ(G) denotes the domination number of G. Let G be a connected planar graph. In this paper, we shall show that if G is free of i-cycles for some i ε 3,4,5,6, then b(G) ≤ 6.