Yury Orlovich - Academia.edu (original) (raw)
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Papers by Yury Orlovich
arXiv (Cornell University), May 27, 2020
arXiv (Cornell University), Jun 25, 2001
It is shown that in star-free graphs the maximum independent set problem, the minimum dominating ... more 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.
arXiv (Cornell University), Nov 29, 2001
For a given finite class of finite graphs H, a graph G is called a realization of H if the neighb... more 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 of H? In fact, there are two modifications of that problem, namely the finite (the existence of a finite realization is required) and infinite one (the realization is required to be infinite). In this paper we show that GNP and its modifications for all finite classes H of finite graphs are reduced to the same problems with an additional restriction on H. Namely, the orders of any two graphs of H are equal and every graph of H has exactly s dominating vertices.
arXiv (Cornell University), May 27, 2020
Journal of Computational Biology, 2021
For a given finite class of finite graphs H, a graph G is called a realization of H if the neighb... more 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 of H? In fact, there are two modifications of that problem, namely the finite (the existence of a finite realization is required) and infinite one (the realization is required to be infinite). In this paper we show that GNP and its modifications for all finite classes H of finite graphs are reduced to the same problems with an additional restriction on H. Namely, the orders of any two graphs of H are equal and every graph of H has exactly s dominating vertices. Comment: 13 pages, 3 figures, in Russian
It is shown that in star-free graphs the maximum independent set problem, the minimum dominating ... more 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.
Electronic Notes in Discrete Mathematics, 2006
Electronic Notes in Discrete Mathematics, 2007
arXiv (Cornell University), May 27, 2020
arXiv (Cornell University), Jun 25, 2001
It is shown that in star-free graphs the maximum independent set problem, the minimum dominating ... more 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.
arXiv (Cornell University), Nov 29, 2001
For a given finite class of finite graphs H, a graph G is called a realization of H if the neighb... more 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 of H? In fact, there are two modifications of that problem, namely the finite (the existence of a finite realization is required) and infinite one (the realization is required to be infinite). In this paper we show that GNP and its modifications for all finite classes H of finite graphs are reduced to the same problems with an additional restriction on H. Namely, the orders of any two graphs of H are equal and every graph of H has exactly s dominating vertices.
arXiv (Cornell University), May 27, 2020
Journal of Computational Biology, 2021
For a given finite class of finite graphs H, a graph G is called a realization of H if the neighb... more 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 of H? In fact, there are two modifications of that problem, namely the finite (the existence of a finite realization is required) and infinite one (the realization is required to be infinite). In this paper we show that GNP and its modifications for all finite classes H of finite graphs are reduced to the same problems with an additional restriction on H. Namely, the orders of any two graphs of H are equal and every graph of H has exactly s dominating vertices. Comment: 13 pages, 3 figures, in Russian
It is shown that in star-free graphs the maximum independent set problem, the minimum dominating ... more 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.
Electronic Notes in Discrete Mathematics, 2006
Electronic Notes in Discrete Mathematics, 2007