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It is shown that in star-free graphs the maximum independent set problem, the minimum dominating set problem and the minimum independent dominating set problem are approximable up to constant factor by any maximal independent set.
For a given finite class of finite graphs H, a graph G is called a realization of H if the neighbourhood of its any vertex induces the subgraph isomorphic to a graph of H. We consider the following problem known as the Generalized Neighbourhood Problem (GNP): given a finite class of finite graphs H, does there exist a non-empty graph G that is a realization… (More)
It is shown that there cannot be any algorithm that for a given nondeter-ministic polynomial-time Turing machine determinates whether or not the language recognized by this machine belongs to P .