Complexity Dichotomies for the Dominating Set Problem

Student: Dakhno Grigorii

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

Educational Programme: Mathematics (Master)

Year of Graduation: 2024

A hereditary class is a set of simple graphs closed under deletion of vertices. Each such class is defined in a unique way by specifying the set of its minimal forbidden induced subgraphs. The dominating set problem for a given graph is to determine whether there is a subset of vertices of a given size such that any vertex not from this subset has a neighbor in it. The main purpose of this graduate work is to determine the complexity status of the dominating set problem for a family of finitely defined hereditary classes, one of the prohibitions of which is a star with three leaves.

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