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# Finding the Maximum Packing of Small Length Paths in Graphs

Student: Artyom Gryaznov

Supervisor:

Educational Programme: Applied Mathematics and Information Science (Bachelor)

In this paper we investigate the problem of packing graphs. Graph packaging is a well-known problem of graph theory, and has many applications in programming and mathematics. In General, three main directions can be distinguished: packing of small-size graphs, packing of graphs with a limited degree of vertices, packing of graphs with additional conditions in permutations. It is believed that the main impetus and one of the major discoveries in the theory of packing of graphs was made by Bollobas and Eldridge in 1978. Also, General information about the packaging of graphs can be found in the literature of Wozniak and YAP. The matching problem (P2-packing) is polynomial solvable. If S has a graph with a connected component of size 3 and more, then the problem is NP-complete . To date, this problem has been studied extensively, there are a large number of approximate algorithms. Currently, the main goal is to develop more accurate algorithms that could work not only for size-limited graphs and packages. Moreover, the desire to reduce the operating time of such algorithms is welcome. In this study developed two approximate algorithm; discussed in detail in the examples; there are counterexamples where the algorithm is not working properly; the experiments of the algorithms on the data graphs with the comparison. This paper also contains the implementation of the developed algorithms in one of the C++ programming languages, screenshots of the program.

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