Connected-domination triangle graphs, perfect connected-neighbourhood graphs and connected neighbourhood sets
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- Минск: БГУ
Abstract
We introduce and characterize the class of graphs in which every connected dominating
set is a (connected) neighbourhood set and the class of graphs whose all connected
induced subgraphs have equal minimum neighbourhood set and minimum connected
neighbourhood set cardinalities. Assuming P - NP, we also prove that the minimum
connected neighbourhood set problem cannot be approximated within a logarithmic
factor in polynomial time in their common subclass, the class of simplicial split graphs