1,674 research outputs found
Upper bounds for the bondage number of graphs on topological surfaces
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
and embeddable on an orientable surface of genus h and a
non-orientable surface of genus k, . 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
The bondage number of graphs on topological surfaces and Teschner's conjecture
The bondage number of a graph is the smallest number of its edges whose
removal results in a graph having a larger domination number. We provide
constant upper bounds for the bondage number of graphs on topological surfaces,
improve upper bounds for the bondage number in terms of the maximum vertex
degree and the orientable and non-orientable genera of the graph, and show
tight lower bounds for the number of vertices of graphs 2-cell embeddable on
topological surfaces of a given genus. Also, we provide stronger upper bounds
for graphs with no triangles and graphs with the number of vertices larger than
a certain threshold in terms of the graph genera. This settles Teschner's
Conjecture in positive for almost all graphs.Comment: 21 pages; Original version from January 201
The total bondage number of grid graphs
The total domination number of a graph without isolated vertices is the
minimum number of vertices that dominate all vertices in . The total bondage
number of is the minimum number of edges whose removal enlarges
the total domination number. This paper considers grid graphs. An -grid
graph is defined as the cartesian product of two paths and
. This paper determines the exact values of and
, and establishes some upper bounds of .Comment: 15 pages with 4 figure
An improved upper bound for the bondage number of graphs on surfaces
The bondage number of a graph is the smallest number of edges
whose removal from results in a graph with larger domination number.
Recently Gagarin and Zverovich showed that, for a graph with maximum degree
and embeddable on an orientable surface of genus and a
non-orientable surface of genus ,
. They also gave examples showing
that adjustments of their proofs implicitly provide better results for larger
values of and . In this paper we establish an improved explicit upper
bound for , using the Euler characteristic instead of the genera
and , with the relations and . We show that
for the case (i.e. or
), where is the largest real root of the cubic equation
. Our proof is based on the technique
developed by Carlson-Develin and Gagarin-Zverovich, and includes some
elementary calculus as a new ingredient. We also find an asymptotically
equivalent result for
, and a further improvement for graphs with large girth.Comment: 8 pages, to appear in Discrete Mathematic
Trafficking of Migrant Workers from Romania: Issues of Labor and Sexual Exploitation
Part of a major research project on the forms of forced labor today developed by the ILO Special Action Programme to Combat Forced Labour (SAP-FL), this paper argues that trafficking for labor exploitation is an emerging issue in Europe and in particular in Romania. Features a detailed comparison of living conditions prior to the emergence of immigration, trafficking, and/or forced labor
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