Methods of Graph Reduction and its' Applications

Student: Sirotkin Dmitriy

Faculty: Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod)

Educational Programme: Data Mining (Master)

Final Grade: 10

Year of Graduation: 2019

For a given graph, the independent set problem is to find the size of a maximum set of pairwise non-adjacent its vertices. There are numerous cases of NP-hardness and polynomial-time solvability of this problem. For determining a computational status of the independent set problem, local transformations of graphs often use. The paper considers some class of replacements of subgraphs in graphs that change the independence number in a controllable way. Some pattern, which is a subset of the power set, defines any such a local transformation. It is gradable. The paper shows that a replacing subgraph exists for any gradable pattern. This results contributes to the algorithmic graph theory and to the theory of constructing graphs with given properties.

Full text (added May 23, 2019)

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