منابع مشابه
Connected Dominating Sets
PROBLEM DEFINITION Consider a graph G = (V,E). A subset C of V is called a dominating set if every vertex is either in C or adjacent to a vertex in C. If, furthermore, the subgraph induced by C is connected, then C is called a connected dominating set. A connected dominating set with a minimum cardinality is called a minimum connected dominating set (MCDS). Computing a MCDS is an NP-hard proble...
متن کاملReconfiguration of Dominating Sets
We explore a reconfiguration version of the dominating set problem, where a dominating set in a graph G is a set S of vertices such that each vertex is either in S or has a neighbour in S. In a reconfiguration problem, the goal is to determine whether there exists a sequence of feasible solutions connecting given feasible solutions s and t such that each pair of consecutive solutions is adjacen...
متن کاملClique-like Dominating Sets
Continuing work by B acso and Tuza and Cozzens and Kelleher, we investigate dominating sets which induce subgraphs with small clique covering number, or small independence number. We show that if a graph G is connected and contains no induced subgraph isomorphic to P6 or Ht (the graph obtained by subdividing each edge of K1;t; t 3), then G has a dominating set which induces a connected graph wi...
متن کاملConnected Dominating Sets
Wireless sensor networks (WSNs), consist of small nodes with sensing, computation, and wireless communications capabilities, are now widely used in many applications, including environment and habitat monitoring, traffic control, and etc. Routing in WSNs is very challenging due to the inherent characteristics that distinguish these networks from other wireless networks like mobile ad hoc networ...
متن کاملDominating Sets in Triangulations
In 1996, Matheson and Tarjan conjectured that any n-vertex triangulation with n sufficiently large has a dominating set of size at most n/4. We prove this for graphs of maximum degree 6.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2016
ISSN: 0012-365X
DOI: 10.1016/j.disc.2016.05.016