Graphs of intersections of closed polygonal chains

• Main Authors: Nikolai P. Prochorov, Ekaterina N. Dul
• Format: Article
• Language: Belarusian
• Published: Belarusian State University 2021-04-01
• Series: Журнал Белорусского государственного университета: Математика, информатика
• Subjects: intersection graph; intersection graph of closed polygonal chains; regular graph; np-completeness; polynomial-time reduction
• Online Access: https://journals.bsu.by/index.php/mathematics/article/view/3379

In the paper such subclass of string graphs as intersection graphs of closed polygonal chains (class of CPC-graphs) was considered, necessary conditions for belonging to that class, forbidden subgraphs and operations with graphs which preserve belonging to the CPC class were found. Considered question about the existence of k-regular CPC-graphs, particularly, pairs (k, n), such that there exists k-regular CPC-graph on n vertexes were found, proved that there are infinitely many k-regular CPC-graphs for any k ∈ N, estimations for the number of k, such that k-regular graph on n vertexes exists, were given. Algorithmic questions in the class of CPC-graphs were investigated. It was proved that independent and dominating set problems, coloring problem and the problem about maximal cycle are NP-hard in the class of CPC-graphs, and problem of recognition of the CPC-graphs belongs to the PSPACE class.