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pro vyhledávání: '"Nikolaev, Andrei"'
Autor:
Nikolaev, Andrei V.
Given an undirected graph $G = (V,E)$, the cut polytope $\mathrm{CUT}(G)$ is defined as the convex hull of the incidence vectors of all cuts in $G$. The 1-skeleton of $\mathrm{CUT}(G)$ is a graph whose vertex set is the vertex set of the polytope, an
Externí odkaz:
http://arxiv.org/abs/2402.13591
We consider the classical minimum and maximum cut problems: find a partition of vertices of a graph into two disjoint subsets that minimize or maximize the sum of the weights of edges with endpoints in different subsets. It is known that if the edge
Externí odkaz:
http://arxiv.org/abs/2302.03935
Autor:
Nikolaev, Andrei
Publikováno v:
Siberian Electronic Mathematical Reports, Volume 19, Issue 2, 2022, Pages 674-687
Pyramidal tours with step-backs are Hamiltonian tours of a special kind: the salesperson starts in city 1, then visits some cities in ascending order, reaches city $n$, and returns to city 1 visiting the remaining cities in descending order. However,
Externí odkaz:
http://arxiv.org/abs/2202.03011
Autor:
Nikolaev, Andrei V., Klimov, Egor V.
A Hamiltonian decomposition of a regular graph is a partition of its edge set into Hamiltonian cycles. We consider the second Hamiltonian decomposition problem: for a 4-regular multigraph find 2 edge-disjoint Hamiltonian cycles different from the giv
Externí odkaz:
http://arxiv.org/abs/2201.03846
Autor:
Kostenko, Andrey, Nikolaev, Andrei
A Hamiltonian decomposition of a regular graph is a partition of its edge set into Hamiltonian cycles. The problem of finding edge-disjoint Hamiltonian cycles in a given regular graph has many applications in combinatorial optimization and operations
Externí odkaz:
http://arxiv.org/abs/2102.12242
We consider a Hamiltonian decomposition problem of partitioning a regular graph into edge-disjoint Hamiltonian cycles. It is known that verifying vertex non-adjacency in the 1-skeleton of the symmetric and asymmetric traveling salesperson polytopes i
Externí odkaz:
http://arxiv.org/abs/2009.04742
Autor:
Nikolaev, Andrei, Kozlova, Anna
We consider a Hamiltonian decomposition problem of partitioning a regular graph into edge-disjoint Hamiltonian cycles. A sufficient condition for vertex adjacency in the 1-skeleton of the traveling salesperson polytope can be formulated as the Hamilt
Externí odkaz:
http://arxiv.org/abs/2001.04683
Akademický článek
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Autor:
Somonov Vladislav, Nikolaev Andrei
Publikováno v:
E3S Web of Conferences, Vol 474, p 02030 (2024)
The article is devoted to the problems that arise for state budget organizations in the management of intellectual property objects created in the field of additive manufacturing in the Russian Federation. The possibilities of their elimination by cr
Externí odkaz:
https://doaj.org/article/e7eba684dadb4b638cec4d340f84f850
Autor:
Kozlova, Anna, Nikolaev, Andrei
We consider 1-skeletons of the symmetric and asymmetric traveling salesperson polytopes whose vertices are all possible Hamiltonian tours in the complete directed or undirected graph, and the edges are geometric edges or one-dimensional faces of the
Externí odkaz:
http://arxiv.org/abs/1901.09651