The bondage number b(G) of a graph G is the smallest number of edges of G
whose removal from G results in a graph having the domination number larger
than that of G. We show that, for a graph G having the maximum vertex degree
Δ(G) and embeddable on an orientable surface of genus h and a
non-orientable surface of genus k, b(G)≤min{Δ(G)+h+2,Δ(G)+k+1}. This generalizes known upper bounds for planar and toroidal
graphs.Comment: 10 pages; Updated version (April 2011); Presented at the 7th ECCC,
Wolfville (Nova Scotia, Canada), May 4-6, 2011, and the 23rd BCC, Exeter
(England, UK), July 3-8, 201