8 papers
Algorithmic methods of finite discrete structures. Topological graph drawing (part III)
Sergey Kurapov, Maxim Davidovsky
The manuscript considers mathematical models for creating a topological drawing of a graph based on the methods of G. Ringel's vertex rotation theory. An algorithm is presented for…
Algorithmic methods of finite discrete structures. Graph clique problem
Sergey Kurapov, Maxim Davidovsky
The monography presents a new algorithm for finding the clique of maximal length in a nonseparable graph. The algorithm is based on the properties of the representation of a clique…
Algorithmic methods of finite discrete structures. Hamiltonian cycle of a complete graph and the Traveling salesman problem
Sergey Kurapov, Maxim Davidovsky, Svetlana Polyuga
The monography considers the problem of constructing a Hamiltonian cycle in a complete graph. A rule for constructing a Hamiltonian cycle based on isometric cycles of a graph is es…
Algorithmic methods of finite discrete structures. Topological graph drawing (part II)
Sergey Kurapov, Maxim Davidovsky
A visualized graph is a powerful tool for data analysis and synthesis tasks. In this case, the task of visualization constitutes not only in displaying vertices and edges according…
Algorithmic methods of finite discrete structures. Topological graph drawing (part I)
Sergey Kurapov, Maxim Davidovsky
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological…
Algorithmic methods of finite discrete structures. Automorphism of Nonseparable Graphs
Sergey Kurapov, Maxim Davidovsky
The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency…
Algorithmic methods of finite discrete structures. Isomorphism of Nonseparable Graphs
Sergey Kurapov, Maxim Davidovsky
In this monography, it is proposed to consider the concepts of spectra of edge cuts and edge cycles of a graph as a basic mathematical structure for solving the problem of graph is…
Algorithmic methods of finite discrete structures. The Four Color Theorem. Theory, methods, algorithms
Sergey Kurapov, Maxim Davidovsky
The Four color problem is closely related to other branches of mathematics and practical applications. More than 20 of its reformulations are known, which connect this problem with…